Theory and Practice of Control and Systems

The following sections are included:

• Organizing and Program Committees

• Preface

• CONTENTS

In this plenary talk we show how a large number of practical feedback design problems, for both linear and nonlinear systems can be reduced to the study of quantified multivariate (multivariable) polynomial inequalities. Three approaches for the study of this class of mathematical problem will be reviewed, symbolic quantifier elimination methods, Bernstein-branch-and-bound methods, and Monte Carlo (probabilistic) methods.

Deadbeat control, a typical example of linear control strategies in discrete-time systems, is shown to be a special case of the pole placement design as well as of the linear-quadratic regulation. This result is obtained by drawing on the parallels between the state-space and the transfer function design techniques.

This paper deals with the problem of Disturbance Rejection by Dynamic Output Feedback. It aims at proposing new geometric and structural characterizations for the Fixed Poles of this problem, i.e. the greatest set of fixed poles that are present in the closed loop system for all possible solution (whatever be the way used to find this solution). We also propose minimal solutions to the problem in terms of the fixed poles, i.e., solutions for which all the poles are freely placed, except the fixed poles of the problem. As a corollary, we propose a structural necessary and sufficient condition for the existence of internally stable solutions, which generalizes the sufficient structural condition proposed by Basile and Marro. It has to be noted that no restrictive assumption is made on the system concerning controllability or observability. Our results are established under the natural and unrestrictive assumption that the overall state description is minimal, i.e. controllable and observable, but with respect to all the inputs (control and disturbance) and all the outputs (controlled output and measurement).

The purpose of this paper is to derive constructive necessary and sufficient conditions for the problem of disturbance decoupling with algebraic feedback. Necessary and sufficient conditions have also been derived for the same problem with internal stability. The same conditions have also been expressed by the use of invariant zeros. The main tool used is the duel-lattice structures introduced by Basile and Marro.

Active suspensions of advanced vehicles allows the active rejection of external disturbances exerted directly on the sprung mass of the vehicle and due to the road surface irregularity. We focus on the road irregularity disturbances with the purpose of isolating the chassis from vibrations transmitted through suspensions. The paper is aimed at the synthesis of a decoupling control law of the regulated outputs, i.e., roll, pitch and chassis height, from the external disturbances. The framework throughout is the geometric approach to the control of dynamic systems. It will be shown that a controlled and conditioned invariant subspace exists and this allows the perfect disturbance localization by feeding back the suspensions heights.

The paper presents a procedure to compute the solution of the Block Decoupling Problems with Coefficients Assignment over a Principal Ideal Domain. The algorithm has been implemented using MapleV.

In this paper, the disturbance rejection problem is solved for structured time-delay system through a graph approach. Ring models of time-delay systems are considered where the entries of the corresponding polynomial matrices are either fixed zeros or polynomials with free parameters. To such systems, so-called structured time-delay systems, one can associate easily a directed graph and study generic properties. The disturbance rejection problem is here revisited by using a graphical characterization of the specific Smith-McMillan form at infinity for time-delay systems in the case of structured time-delay systems.

This paper deals with the generic number of zeros in the context of linear structured systems. For such systems, the entries of the state space model matrices are supposed to be either fixed zeros or free parameters. A directed graph can be associated to such systems and structural properties can be studied, i.e. properties which are valid for almost all values of the free parameters. The notions of decoupling zeros, transmission zeros and system zeros are analyzed for such systems. The outcomes of this paper extend previous works on structural zeros but without the assumption that all states are input and output connected.

We consider the application of a new adaptive control design algorithm to nonlinear continuous chemical proceesses with uncertainty. This new algorithm is based on the fundamental ideas of the adaptive backstepping approach, and allows one to design dynarnical adaptive compensators for the regulation of observable minimum phase nonlinear systems without the requirement of previous transformation into canonical forms. The validity of this approach is demonstrated via computer simulations.

The management of fire emergencies in a complex system, whose insufficient functional knowledge is available, is the case study.

Genetic algorithms provide the training data for a neurofuzzy controller in order to translate the knowledge of the optimal management from the genetic physical support into a fuzzy-logical one. The genetic agent looks over the variables and parameters offered by a model of the plant; because of the limits imposed on the sensors and instrumentation, the neurofuzzy controller's input variables belong to a subspace of the variables concerning the model; the inference, created inside the controller, has to overcome such a lack of information.

The set of the generated rules is so large that it can be used to build a fuzzy controller, not to increase the knowledge of the operators concerning the plant. The complexity of the system as well as of the objective to achieve, requires the neuro-fuzzy controllers to be case specific and the number of rules to be elevated.

Meanwhile, the riskiness and the dynamics of emergencies demand the inference available for the operator to be general, containing a few, clear and intuitive rules. A neural method of rule compression and generalization for training the operators is thus proposed and discussed.

In almost every industrial application that requires high actuation forces and needs actuators with a significant high power density hydraulic actuators are used. Despite these actuators have highly nonlinear model characteristics they commonly are controlled by linear feedback controllers in practical use. This paper introduces an applicable nonlinear control concept for hydraulic differential and synchronizing cylinders which uses a cascaded control concept based on exact linearization. Theoretical and experimental results are presented.

In the following the observer design for highly nonlinear plants is discussed. The main focus is on hydraulic cylinders, which are of great interest e.g. for trajectory tracking of heavy-duty and elastical robots. The road to success is a combination of axiomatic and empiric approach for the plant modeling. This yields a simple and at the same time accurate model, which can be used for the observer design. In This paper mainly bilinear observers are designed and applied to a hydraulic differential cylinder. For this example experimental result at the test-bed will verify the theoretical considerations.

This paper deals with the design of a plasma current and shape feedback control system for the International Tokamak Experimental Reactor (ITER).The controller is composed of two parts: an H_∞controller, whose outputs are the poloidal field coil currents, and a second controller which, driving the poloidal field coil voltages, forces the currents to track the trajectories dictated by the H_∞controller. The resulting design procedure can be casted in the block back stepping framework. The simulation results show that the proposed controller guarantees good closed loop performance without violating the many existing constraints on the control signals.

Consider a sequence of events in the event space of a system whose I-O relation is given by a convolution operator. We define the concepts of sequential controllability and uniform sequential controllability for these systems. In general, uniform sequential controllability implies sequential controllability but the converse is not true in all such systems. We investigate proper restrictions on the impulse response function of these systems, under which the converse of this statement is also true for the cases in which the controls of system are restricted to be in the unit ball of the L_∞ space. Then, we apply this property to generalize some of the results published by Honig et al.⁶ related to a certain signal separating problem in digital communications in which the input signals are bounded in amplitude and the receiver has a finite precision. First, we present a class of input signals called generalized bit-by-bit signaling (GBBS), which provide a “feasible solution” to the problem. Secondly, we characterize certain class of impulse response functions for which the GBBS is an optimal solution to the problem. This in turn shows that the conjecture of Honig et al. mentioned in ⁶ is true for a rather large class of impulse response functions. The MCT (Maximum Channel Throughput) of the channels whose impulse response functions are in this class will be computed as well.

Inaccurate knowledge of the tool's position-reference is a major source of errors in precision turning. This paper presents an automated concept of establishing such reference with respect to the machine using a feedback from a diffraction instrument. In the tool's home position, its tip and a fixed blade form a diffraction slit that is imaged onto a linear CCD array. With special processing to obtain sub-pixel resolution, the dark and light diffraction bands determine the width of the slit and thereby the tool-tip position. Detected deviations from the expected position (few microns range) arc compensated by the programmed adjustment of the radial feed. While this compensates for much of the machining error (tool wear, thermal deflections, unassignable causes…), errors due to the elastic deflections of the machine-workpiece-tool system remain unavailable. Hence, this feedback has been supplemented by an on-machine dimensional inspection of the part whereby the tool itself acts as a probe of a “fine touch” contact (and proximity) sensor. Work in progress is thus monitored between successive tool passes without affecting the work setup, allowing compensation, in the subsequent cutting pass, of the machining error that arc due to the elastic deflections. The application of this concept is illustrated on the example of cutting a groove inside a narrow hole where by the tool wear, thermal deformations and elastic deflections arc all significant sources of errors.

We consider a scalar 1st-order nonlinear differential equation with a delayed relay-output proportional feedback. We show that, under a boundedness condition on the nonlinearity only, any solution of this equation has asymptotically a finite number of zeros on compact sets. We provide an estimate of the time after which the super-high-frequency disappears. This improves some previous works by Shustin. As a consequence, using some works by Fridman et al., any solution of the system under study is attracted towards one of the periodic solutions.

In this paper the digital implementation of a second order sliding mode control proposed in previous papers is presented. The sampling period δ is considered as an intentional nonideality in the control law such that only a O(δ²)-vicinity of the sliding manifold can be reached. Taking into account a class of uncertain nonlinear system, by mean of a suitable multirate sampling technique, an estimate of the uncertain dynamics is available so that the performance. of the real sliding behaviour are increased, and a O(δ³) boundary layer is attained. Furthermore, such estimate allows for the decreasing of the control effort, which, combined with the second order sliding mode approach, leads to the avoidance of the ringing phenomenon.

Robust stabilization of a fairly general class of discrete-time nonlinear systems (input affine NARX models), in Presence of uncertainties and/or external disturbances, is here addressed. A control algorithm is presented based on Discrete-time Variable Structure Control. A nonlinear sliding hyperplane is used to allow the exact imposition of the sliding condition also inside the switching sector. Simulation results are also reported.

Sliding mode is used in order to retain a dynamic system accurately at a given constraint and features theoretically-infinite-frequency switching. Regular sliding modes are known to feature finite time convergence, precise keeping of the constraint and robustness with respect to internal and external disturbances Having generalized the notion of sliding mode, higher order sliding modes preserve or generalize its main improve its precision with discrete measurements and remove the chattering effect. However, in their standard form, most of 2-sliding controllers are sensitive to measurement error. A special measurement step feedback is introduced in the present paper, which solves that problem without loss of precision. The approach is demonstrated on a so-called twisting algorithm. Its asymptotic properties are studied in the presence of vanishing measurement errors. A model illustration and simulation results are presented.

This paper presents a method for the design of asymptotically stable sliding observers for linear multivariable systems. The design ensures that in the presence of unmatched uncertainty, the estimated state nearly approaches the actual state. Certain sufficient conditions should be satisfied for the asymptotic stability of the error system.

An obstacle avoidance system based on sonar data is described. The system is conceived for operating on an Autonomous Underwater Vehicle during navigation near to the sea bottom. The performances of the system have been evaluated on real sonar images and results are reported and discussed.

The coordinate motion of a team of mobile vehicle is considered. The problem is set up in a team-theory framework and solved via a hybrid approach which allows for a low-level steering strategy and for a set of distributed neural supervisors able to define the ‘escape’ strategy when a situation of ‘congestion’ (implying the need of some coordination) is detected.

We address the localization problem in unstructured environments for a nonholonomic mobile robot equipped with exteroceptive sensors. The usual approach to robot localization is to adopt the Extended Kalman Filter (EKF), which results in a typical predictor-corrector structure. The use of the EKF, as opposed to the standard Kalman Filter, derives from the nonlinearity of the robot kinematic model as well as of the observation function. In order to avoid at least the first linearization error, we propose to take advantage of the possibility of transforming the original kinematic system in chained form through an appropriate feedback transformation. The obtained equations are closed-form integrable, thereby yielding a linear discrete-time model which provides exact odometric prediction and associated covariance. Another advantage of our approach is that the stochastic description of the noise in the chained-form coordinates is more natural. The performance of the proposed localization method is illustrated through simulations on a mobile robot having the kinematics of a unicycle and equipped with ultrasonic sensors.

The environment map used by a multirobot system should be constructed exploiting all the information carried by the sensor equipment associated with each component of the system. In this paper the multirobot system acquires the environment data through a set of sonar sensors. Three different techniques are proposed here to fuse together the information acquired by each single system component. The purpose is that of obtaining a global environment map increasing the reliability and accuracy of the sonar measures.

In this paper, we consider the problem of localizing a mobile vehicle moving in an unstructured environment, based on triangulation measurements derived from processed optical information. The problem is shown to be intrinsically nonlinear, in the sense that the linear approximation of the system has different structural properties than the original model. In particular, linearized approximations are non-observable, while results obtained from differential-geometric nonlinear system theory prove the possibility of reconstructing the position and orientation of the vehicle and the position of the obstacles in the environment from optical information.

The paper presents a hierarchical navigation system for an autonomous mobile robot, specifically designed for indoor environments. Among all the elements comprising the system, specific attention is given to the environment description, to the multi-sensor based positioning system, and to the motion planning algorithm. Complex, and partially known, indoor environments are modeled by means of a flexible hierarchical data structure. The motion planning algorithm is based on the concept of configuration space. Exact Cell decomposition is used to derive a description of the free space, and graph search took are then used to compute a possible path. The sensory system is based on the joint use of an encoder based odometer, of a vision system, and of an ultrasonic captor sensory system.

The aim of this paper is to explore a possible approach to the problem of designing control and diagnostic strategies capable of satisfying customer and regulatory demands for future generations of powertrains. The work described in this paper focuses on the use of physical models to estimate unmeasured or unmeasurable variables and parameters, to be used for control and diagnostic purposes.

In this paper an indicated torque estimation procedure, based on a dynamic model of an N-cylinder IC reciprocating engine, is presented. Torque estimation is performed by implicitly inverting the dynamic model, via a non linear sliding mode observer. Experimental tests have been conducted on a two-cylinder Diesel Engine, proving the feasibility of this approach.

In order to regulate and control a real system, a mathematical representation is required which provides a satisfactory estimation of the process and which can be obtained by Identification. System identification is the subject of much research and many articles propose often complex discreate algorithms. Moreover. the models and identification methods used are different according to whether the real system is linear or nonlinear. This paper presents identification methodology based on a single model deduced from network theory. The first paragraph proves end defines the model which allow identlfication of a real complex process, whether it be linear non linear The following paragraph describes the method of calculation for a polynomial model as an alternative to a static data base representatlon (Internal combustion engine map).

For each model, it measures and analyses the degree of precision obtained and defines the Influence parameters for convergence of network errors.

In the field of automotive application turbocharged Diesel engines Are more and more widely used due to the very low values of specific fuel consumption they allow for. However, the tight emissions limits recently defined are going to force the introduction of specific and proper techniques and solutions. As a consequence, the engine has become a complex plant whose performance is strongly influenced by the behavior and interactions between different components and system (e.g, fuel injection system, intake and exhaust manifolds exhaust gas recirculation system turbocharger, aftertreatment components).

The need of a proper management system, which allows to take advantage of the available control parameters, is therefore apparent also for Diesel engines. with the aim to study the effects of control parameters on engine behavior and to define engine management strategies, a simplified theoretical model has been developed to simulate a DI turbocharged Diesel engine fitted with an exhaust gas recirculation system (EGR). In the paper the model is presented, together with some theoretical results which are analysed and compared with experimental data measured on a typical automotive Diesel engine.

The structure of a hierarchical system of models for model based optimization and rapid prototyping of control strategies in automotive spark ignition engines is presented. The advantages of a distributed and hybrid modeling approach are discussed, in order to meet the conflicting goals of high flexibility and precision with limited experimental cost and computational time.

The critical role played by the identification phase is discussed, and a comparative analysis of the estimation procedures adopted during model validation is presented, analyzing their connections with the model development process.

For the precise control of fuel injection in internal combustion engines, a fundamental issue is the correct estimation of the amount of air trapped into the cylinders; this requires a modeling tool able to yield accurate on-line predictions.

A novel formulation for the air induction processes has been developed, in terms of a quasi-propagatory, lumped parameter model. The model has been tested for a number of transient situations, displaying correct predictions in spite of very limited computing resource.

For linear delay system the disturbance decoupling problem is studied. The structural approach is used to design a decoupling precompensator. The realization of the given precompensator by static state feedback is studied. Using various structural and geometric tools, a complete description of feedback is given, in particular, derivative of the delayed disturbance can be needed in the realization of the precompensator.

In this paper, the passivity definition which has been set during the seventies, for state space representation of finite dimensional electrical circuit dements, will be extended to infinite dimensional state space representations of generalised network “elements”, using a semigroup approach. A characterisation of passive elements, using the positive real property, will be derived, as well as a more convenient (but only sufficient) condition of passivity, based on the coercivity of the hermitian part of the input-output transfer function. This last condition will then be applied to the case of a linear system with delay.

In previous papers the authors presented an elementary theory for feedback control of nonlinear delay systems, in which methods of standard nonlinear analysis were used to solve control problems such as output regulation and tracking, disturbance decoupling and model matching for a class of nonlinear delay systems. Output control was obtained by means of state feedback control laws, but nothing was said about the behavior of the system state. In this paper some results have been obtained about this problem. It is proved that if the output and its derivatives up to a given order are driven to zero, and if the system owns a certain Lipschitz property in a suitable neighborhood of the origin, and the initial state is inside such neighborhood, then the system state asymptotically goes to zero. Simulations on nonlinear delay systems unstable in open loop match the theoretical results.

A method of identification and control for Wiener-type nonlinear process which has input time delay is devised. Data from a relay feedback experiment is used. The static nonlinearity part of the model is represented by an invertible function defined on an operation range. Parameters in this function is determined by an simple optimization procedure which aims at obtaining a symmetric cycling instrumental output. Based on the instrumental output, a simple transfer functions of first order or of second order is determined. The apparent dead time together with the apparent time constants is determined by a simple trial-and-error procedure. Notice that identification of linear and nonlinear part are fully decoupled. Control of such processes using the identify model is then presented. A desired instrumental output trajectory is first determined from a given set-point command for the output. A controller that makes the instrumental output to follow the resulting trajectory is then synthesized.

Multivariable nonlinear systems with time delays are considered. The delays are supposed to be constant but not commensurate. The goal of this paper is twofold: first to give a structure algorithm which displays some system invariants, second to solve control problems such as disturbance decoupling.

In this paper, a finite dimensional approximate model of a slewing flexible beam is proposed, which is parametric in the approximation order, so that a prescribed accuracy in the representation of the mechanical system can be easily obtained. A simple PD control law, which requires only the measurement of the motor position and velocity, is shown to globally asymptotically stabilise all the flexible modes considered in the approximate model, regardless of the chosen approximation order. Experimental results show the effectiveness of the proposed control law in achieving both position regulation and vibration control.

In this paper we address the design of a controller-observer for a mechanical crane. We consider a linear model of the crane where the lenght of the suspending rope is a time-varying parameter. The set of models given by frozen values of the rope lenght can be reduced to a single time-invariant reference model using a suitable time scaling. We construct a controller and an observer for the reference model assigning the desired closed loop eigenvalues for the both system and estimation error. The time scaling relation can be inverted to derive the corresponding controller and observer law for the time-varying system. This law takes the form of a gain-scheduling as a function of the rope length. The proposed procedure leads to the computation of the desired time-varying gains for controller and observer design in a symbolic parameterized form. Using a Lyapunov-like theorem, it is possible to find relative upper bounds for the rate of change of the time-varying parameter that ensure the stability of the original system.

The optimal positioning of sensors and actuators for the control of flexible structures is discussed in this paper. A class of performance criteria based on controllability/observability measures is analyzed and a solution framework based on genetic programming is proposed. Problems with both continuous and discrete search spaces are solved within the devised scheme, and multimodality is exploited in order to determine not only the “best” solution but also a family of “good” relative optima.

In this paper an analysis is carried out in order to design robust controllers for flexible links with uncertain flexible dynamics. In particular, reference has been made to the extreme condition in which the whole flexible dynamics is unknown. A Low Authority /High Authority Control scheme has been considered. The inner loop, implemented using a PD regulator, makes the controlled system asymptotically stable; the external loop, implemented using an H_∞ controller, ensures robust performances. The robustness is referred to real plant uncertainties, which are taken into account during the design phase. Some improvements are also been tried, in order to improve the control system performances.

Implicit systems of partial differential equations arise in modelling infinite dimensional systems such as cables and rods. Whenever the Physical system is modelled as inextensible (i.e. no elasticity is assumed in the model), numerical problems may occur, due to constraints imposed on the state variables. This paper discusses different models of inextensible cables, referring to a suitable definition of the index of the system of partial differential equations. The index is used to qualify the properties of the different formulations with respect to the feasibility of the integration, by means of available numerical solvers. Guidelines for the index reduction of a higher index model are offered as well.

In⁵ algorithms are presented for analytic gain and phase margin design. Without special care however, the compensator computed with this algorithm is not a real rational function. In³ it is shown that with some care, a real rational compensator for phase margin design can be computed from the theory in ⁵. In this paper both gain and phase margin problems are reduced to interpolation problems with positive-real functions, which saves a step in the algorithm given in⁵, where interpolation is done with bounded-real functions, in the case of gain margin design.

In this paper we consider a linear system subject to norm bounded, bounded rate time-varying uncertainties. Necessary and sufficient conditions for quadratic stability of such class of uncertain systems are well known in the literature. Quadratic stability guarantees uniform exponential stability in presence of arbitrary time-varying uncertainties; therefore it becomes a conservative approach when, as it is the case considered in this paper, the uncertainties are slowly-varying in time. The contribution of this paper is that of giving sufficient conditions for the exponential stability of the system taking into account the bound on the rate of variation of the uncertainties; therefore such condition will result a less conservative analysis tool than the quadratic stability approach.

A Youla-parameterisation can be used to improve the disturbance rejection properties and robustness of a linear control loop with no constraints on the system inputs/outputs. However, so far it has not been clear how such a parameterisation might be used during constraint handling (implying a non-linear control law) common with predictive control. Here we show how a fixed Youla parameter can be used to advantage even during constraint handling hence improving the performance of a predictive control scheme significantly.

A previous paper by the same authors presented a general theory solving (finite horizon) feasibility and optimization problems for linear dynamic discrete-time systems with polyhedral constraints. We derived necessary and sufficient conditions for the existence of solutions without assuming any restrictive hypothesis. For the solvable cases we also provided the inequative feedback dynamic system, that generates by forward recursion all and nothing but the feasible (or optimal, according to the cases) solutions. This is what we call a dynamic (or automatic) solution. The crucial tool for the development of the theory was the conical approach to linear programming, illustrated in detail in a recent book by the first author. Here we extend this theory in two different directions. The first consists in generalizations for more complex constraint structures. We carry out two cases of mixed input state constraints, yielding the dynamic solution for both of them. The second case is particularly interesting because it appears at first sight hope leas, but, again, resort to the conical approach provides the key to overcome the difficulty. The second direction consists in evaluating the possibility of obtaining at least one solution to problems in the present class, by means of linear, instead of inequative, feedback. We illustrate three mechanisms that exclude any linear solution. First the linear feedback cannot handle cases where the origin is in the constraining set for the state. Second the linear feedback lacks the initial condition independence of the inequative solution. Third the linear feedback cannot control the geometric multiplicity of eigenvalues of the system, and this prevents stabilization, when the constraint structure is such that we cannot allow the state to converge to the origin. These results clearly strengthen the significance and relevance of the theory of linear (optimal) regulator.

In this paper we consider the problem of stabilizing a dynamic system by means of bounded controls. We show that the largest domain of attraction can be arbitrarily closely approximated by a “smooth” domain of attraction for which we provide an analytic expression. Such expression allows for the determination of (non-linear) control laws in explicit form.

A predictive controller robust against persistent disturbances is presented for discrete-time linear time-invariant constrained systems. It is known that the action of a bounded disturbance on a nominally designed predictive control loop can affect feasibility and consequently produce a dramatic degradation of performance: in certain cases even an unbounded state behaviour can occur. To overcome this difficulty, the notion of controlled dirturbance (cd) invariant set has been used. The proposed controller is based on constrained optimization of a nominal (disturbance-free) performance index with the additional constraint that the future state will lie in a prescribed cd-invariant set whatever disturbance may have occurred. As a result, both bounded-disturbance-bounded-state stable behaviour and constraint fulfillment are guaranteed.

In this paper the problem of stabilizing linear discrete-time systems under state and control linear constraints is studied. Many formulations of this problem has been given in the literature. Here we consider the case of finding a linear state feedback control law making a given polyhedral set in the state space positively invariant while the control remains bounded within prefixed values. Necessary and sufficient conditions for the existence of a solution of the problem are given in terms of polyhedron's vertices and directions. These conditions lead to a set of linear constraints which can be solved using linear programming techniques. This approach has been used by several authors and the difference which characterizes the result of this paper is the choice of an alternative objective function. Such function is the natural outcome when describing the constraints in terms of polyhedron's vertices and directions.

In this paper an integrated robust identification and control design procedure is proposed. It is supposed that the plant to be controlled is linear, time invariant, stable, possibly infinite dimensional and that input-output noise corrupted measurements are available, together with some general information on the plant and on the characteristics of the noise. The emphasis is placed on the design of controllers guaranteeing robust stability and robust performances, and on the trade off between controller complexity and achievable robust performances. First, an uncertainty model is identified, consisting of a parametric model and a frequency bound on the magnitude of the modeling error, accounting for the dynamics not modeled by the parametric model. Second, a robustly stable controller satisfying given H_∞ performance specifications is designed using H_∞ optimization techniques. Third, the robust performances of the designed controller are computed, allowing to determine the level of model complexity needed to guarantee desired closed loop performances. Numerical examples illustrate the effectiveness of the proposed design procedure.

We present a numerical study for an identification problem governed by a Volterra integral equation arising in heat flow. This complements the abstract approximation theory developed by Aizicovici et al.

This article discusses new results regarding a nonlinear control design framework that is suitable for a claw of distributed parameter systems with uncertainties. In particular we focus on a temperature field control (heat equation) problem in a welding application. The control objective in first formulated as a function of the system state and a control is sought such that the set in the state space where this relation is true forms an integral manifold reachable in finite time. This manifold is called a Sliding Manifold. The Sliding Mode controller implements a high (theoretically infinite) gain, which serves as a tool to suppress the influence of matched disturbances and uncertainties in the system behavior. The theory is developed generically for systems in the Jordan canonical form. The controller manifold design is described in detail; the observer manifold design can be achieved in a dual manner. Simulations of a heat equation are included and an experimental setup is briefly described.

In many applications involving PDE models it is standard engineering practice to replace the PDEs by a finite dimensional system of ordinary differential equations. Sometimes this approximation forms a differential algebraic equations (DAE). Recently it has been recognized in several areas that the choice of approximation needs to take into account the numerical and analytic properties of the finite dimensional DAE approximation. In this paper we examine how to recognise when simulation difficulties are due to the approximation or modeling as opposed to being intrinsic difficults of the problem being considered. Intuition and illustrative examples are stressed as opposed to detailed theoretical results.

The spectral approach to nonlinear filtering is generalized to the case of distributed observation. Convergence to the optimal filter is shown for an approximate scheme based on this approach, and the error of approximation is estimated.

Many inverse problems of practical interest are ill-posed in the sense that solutions do not depend continuously on data. To effectively solve such problems, regularization methods are typically used. One problem associated with classical regularization methods is that the solution may be oversmoothed in the process. We present an alternative “local regularization” approach in which a decomposition of the problem into “local” and “global” parts permits varying amounts of local smoothing to be applied over the domain of the solution. This allows for more regularization in regions where the solution is likely to be more smooth, and less regularization in regions where sharp features are likely to be present. We illustrate this point with several numerical examples.

The chattering phenomenon is the major drawback in sliding mode control of real system. In this paper the authors extend to some classes of uncertain multi-input systems an unchattering variable structure control scheme, previously presented for the single input case, based on second order sliding modes. In particular, the use of a simple estimator and of a hierarchical structure of second and first order sliding surfaces allows for reducing a large class of uncertain multi-input systems to a simpler one for which the extension of the single input case is straight forward.

This paper studies the application of two tracking control schemes, namely sliding mode control and dynamical back stepping with sliding, to a dc-to-dc boost converter. Both approaches are based on the specification of a switching control law which accomplishes indirect asymptotic sinusoidal voltage tracking. The exposition emphasizes the use of Fourier expansions in solving an ordinary differential equation of the Abel type, and sliding backstepping design using BACKDSMC, a symbolic algebra MATLAB toolbox.

Sliding mode is used in order to retain a dynamic system accurately at a given constraint and is the main operation mode in variable structure systems. Such mode is a motion on a discontinuity set of a dynamic system and features theoretically-infinite-frequency switching. The standard sliding modes are known to feature finite time convergence, precise keeping of the constraint and robustness with respect to internal and external disturbances. In realization their sliding precision is proportional to the time interval between measurements. Having generalized the notion of sliding mode, higher order sliding modes preserve or generalize its main properties and remove the chattering effect. With discrete measurements r-th order sliding mode realization may provide up to the r-th order of sliding precision with respect to the measurement interval. A sample of an arbitrary-order sliding mode attracting trajectories in finite time and featuring the above-mentioned utmost accuracy is demonstrated for the first time in the present paper.

The output regulation problem is considered in the two cases of static SM control of nonlinear systems with state feedback, and dynamic SM control of linear systems with error feedback. Both minimum and nonminimum phase plants with relative degree one are considered, and the external disturbance (or reference) is modelled as a neutrally stable exogenous system.

A neural-adaptive sliding mode control system for a class of discrete-time nonlinear plants is proposed. Neural networks and adaptation are required to ensure that a desired discrete-time sliding manifold is approached asymptotically, in spite of the nonlinear and unknown plant dynamics. The sliding mode control law used is of the non-switching type and an augmented error adaptive approach is taken. The effect of the inevitable non-zero approximation accuracy of the neural network on system stability is taken into consideration by using dead-zone adaptation. Stabiity and convergence proofs are presented.

The use of a multi-input control design procedure for uncertain nonlinear systems expressible in multi-input parametric-pure feedback form to determine the control law for a class of mechanical systems is described in this paper. The proposed procedure, baaed on the well-known backstepping design technique, relies on the possibility of extending to multi-input uncertain systems a second order sliding mode control approach recently developed, thus reducing the computational load, as well as increasing robustness.

This paper presents the control of an under actuated two link robot called the Pendubot. We propose a controller for swinging the linkage and rise it to its upper most unstable equilibrium position. The balancing control is based on the passivity properties of the system, as it has been done for the inverted pendulum in Lozano and Fantoni.

This work describes, via examples, a possible approach to the exponential stabilization of nonlinear systems with nonstabilizable first approximation. The notion of initialized discontinuous state feedback dynamic controller and the definition of quasi-exponentialstability are introduced and discussed. The proposed control laws are discontinuous as a function of the state of the controller, but are smooth as a function of the state of the plant. The problems of quasi-exponential stabilization for the Brockett integrator and for the Euler equations with two controls are discussed in detail.

This paper investigates the application of a recently developed gain scheduling technique to the control of the radial positioning servo system in a compact disc (CD) player mechanism. In this application the gain of the plant and the disturbances affecting it depend on the operating point of the system. We model this situation with a linear parametrically-varying (LPV) generalized plant where the performance specifications vary according to the operating conditions. Our purpose is to show in how far stability and performance can be guaranteed through the design of an LPV controller.

A robust output feedback control problem can be formulated as a min-max optimal control with imperfect information. The main difficulties for non linear-quadratic cases come from the computation of the information state and the certainty equivalence principle which is not always valid. Nevertheless, for a class of nonlinear systems stabilizable by state feedback and observable for any known bounded disturbances, and for which there exists an observer with some monotonicity properties, we show how to derive a class of finite dimensional controllers that stabilize the system in presence of unknown disturbances. This result is illustrated by an application to a biological waste treatement process.

The paper presents the implementation of an impedance control scheme for the govern of an in-parallel actuated robotic platform: the basic characterisation of the controller is assessed by means of computer simulation, once the complete dynamic model of the parallel rig has been duly worked out. Some simulation results are briefly commented, showing the behaviour of the controller: actually, cooperative set-up of two manipulators enhances the performance of the system for some application tasks, as shown in related papers.

The main reasons one might prefer the design of a controller in the frequency domain rather than in the state space are the possibility of tuning directly sensitivity and performance, i.e. complementary sensitivity, and the fact that the resulting controller is not based on any kind of observer. Further more, robustness of the controller with respect to both unstructured and structured perturbations can be explicitly used as design parameters. The disadvantages lies in the fact that such a compensator for the plant normally inverts the plant dynamics. As long as the plant dynamics are well damped, the inversion of the dynamics is a practicable way for changing both sensitivity and performance of the closed loop. Of course, weakly damped stable plant modes cannot be canceled by the control law since the resonance frequency is never exactly known. The challenge is to find a weighting scheme which conserves the advantages mentioned above but without the inversion of the plant.

The loop shifting of the closed loop plant is performed using ℋ_∞ minimization algorithms. The first part focuses on the S/KS/T scheme and its plant inversion properties. In the second part, a two step controller design is presented. In a first step, an inner control law is designed. Its only task is to dampen the roots near the imaginary axes. Bandwidth and gain will stay rather untouched during this design step. Appropriate rules for choosing the weights such that the resulting controller only acts on the damping of the modes will be given. In a second step, the sensitivity and performance of the final closed loop is tuned using a standard S/KS/T design scheme. This is possible since we assume that all modes are well damped by the inner control loop. Finally a controller is designed using the presented methodology and implemented on a flexible shaft system.

This paper focuses on the Popov generalized theory for a class of linear systems including discrete and distributed delays. Sufficient conditions for stabilizing such systems as well as for coerciveness of an appropriate quadratic cost are developed. The obtained results are applied for the design of a memory less state feedback control law which guarantees the closed-loop stability with an ℒ₂ norm bound constraint on disturbance attenuation.

The output control problem for multi delays nonlinear systems is considered in this paper, and a solution is proposed for delay minimum phase systems. In paper [9], through the use of a suitable formalism, we showed a solution to the problem of the input-output linearization via static-state feedback for a single delay class of nonlinear delay systems. In this paper by generalizing the concept of delay relative degree, we obtain the linearization of the input output mapping for multi-delays nonlinear systems, such that the output can be easily controlled. Moreover a theorem is proven which assures that under certain hypotheses also the state goes to zero, if the output is driven to zero by the methodology here presented. Simulation 4 results on an unstable nonlinear two delays system are also reported showing the effectiveness of the proposed method.

This paper considers the pole placement in multivariable systems involving known delays by using dynamic controllers subject to single rate multirate sampling. The controller parametrizations and auxiliary compensating signals to deal with the contribution of the delays are calculated from systems of algebraic equations which are solved by using the Kronecker product of matrices.

The use of rational approximations to time delay block is considered in the context of the realization of Smith predictors, either in continuous-time or in a sampled-data setting. An overall view is composed with the discussion of dead-time compensation in general, Smith predictor properties, approximate modelling of time delay systems and the benefits of implementing approximate Smith compensators. Arguments on the robustness and feasibility of these close the paper.

A methodology for H_∞ observer design is proposed for linear systems with delay in state and output variables. The designing methodology involves attenuating of disturbance to a prespecified bound. The observer design requires solving certain algebraic Riccati equation. Some examples are given in order to illustrate the proposed methodology.

The development and the identification of a model for the analysis of an aero-derivative gas turbine power plant employed in natural gas pipeline stations are presented. The purpose is establishing a method for prediction and remote monitoring of pollutant emissions, in particular nitric oxide, starting from the operating data provided by the usual gas turbine control unit.

Thermodynamic models of both plant and components are employed, including a chemical kinetics based simulation of NO formation. The full set of thermal cycle parameters is identified via proper optimisation techniques, starting from a limited set of operating data. A good agreement with experimental data is achieved. In addition, unreliable operating data can be interpreted and detection of either component or sensor fault is allowed. Continuous on-line prediction of both performance and emissions during the normal gas turbine operation, when only the normal control unit is active, can be then achieved. Some preliminary results obtained by use of components matching approach are also presented, and the potential advantages discussed.

The methodology can be also considered a basis for the definition of strategies for part-load operation planning and load sharing between several gas turbine units, with the objective of minimum pollutant emission.

In this paper an application of a procedure for the detection and isolation of abrupt changes (such as faults) in input-output control sensors of a single shaft industrial gas turbine is presented. The system considered is modeled as a linear dynamic system corrupted by stochastic additive noise. The diagnasis system involves the design of Kalman filters with unknown inputs and uses statistical tests on filter innovations. The results are compared with the ones suggested in a related work and obtained by using model-based observers and a geometrical analysis of residuals.

This paper presents a method to obtain a model incidence matrix with a column-canonical structure (i.e., in which each matrix column has the same number of zeroes, but in different positions). This particular matrix structure is used in a parity equation-based diagnostic technique, in order to achieve a robust method for the high-threshold isolation of single faults in gas turbine sensors.

The incidence matrix with canonical structure was obtained by using a number of ARX (Auto Regressive exogenous) MISO (Multi-Input/Single Output) models equal to the number of gas turbine measured outputs, each model calculating an estimate of one measurable output as a function of other inputs or outputs measured on the machine.

Once the model incidence matrix with column-canonical structure was obtained, tests were performed in order to find the minimal sensor faults that can be detected and isolated.

The results of some experimental tests aimed to analyze the overall efficiency of the One-Step-Ahead adaptive control technique, applied to hydraulic transmissions, are presented. Moreover, the experimental results obtained by means of the One-Step Ahead adaptive algorithm are compared with those obtained by using two classical control techniques, the Proportional and the Proportional Integral techniques. Such a cornparison outlines the superior control characteristics of the One-Step-Ahead adaptive algorithm.

In the last years a hierarchical model structure has been developed by the authors for the optimal design of engine control strategies. This structure is composed of a group of models based on different approaches ranging from fast black-box models to phenomenological ones. The black-box models together with grey-box mean value dynamical models are linked with the computer code O.D.E.C.S. which is used in industrial environment for the optimization of engine control strategies.

In the framework of black-box models development, some approaches have been considered in order to enhance model precision and to maximize the level of information derivable from experimental tests. The former set of models is based on classical regression techniques to compute steady state engine performance (i.e. fuel consumption and HC, CO, NO_X emission levels) together with interpolation techniques in order to evaluate performance in the domain not investigated during experimental tests. To overcome some limitations coming out from the use of regressions and interpolation techniques, a Neural Network model structure has been developed. The Neural Networks, well suited for non linear phenomena modelization, are able to deal with high uncertainty input level (independent data variables) or noised data as well as are able to operate outside their range of training experience. For the purpose of the present application a Multi Layer Perceptron (MLP) Neural Network structure has been selected with a Backpropagation training procedure.

The results of simulations obtained by using the Neural Network model developed are compared with the previously used regression technique and the advantages emerging from the new approach are discussed.

This paper reports the results of an experimental study of a vision-based controller for an industrial robot. An image acquisition system with fixed camera is employed and a suitable calibration algorithm of camera parameters is carried out. An image based visual servoing strategy is pursued to achieve end-effector position regulation directly in the image space, the actual control law being of simple PD type. A number of case studies are developed, and the robustness to imperfect manipulator Jacobian and/or camera orientation is extensively tested.

This paper describes a new approach to vision-based navigation control in unstructured environments. The potential application devised is that of an AMR (Autonomous Mobile Robot) transporting medical instruments in a hospital, but similar tasks, like pallets transport in industrial environment, would benefit of the proposed approach. The method combines the information derived from internal odometry and from images collected by a single camera mounted on-board. The key problems faced in the paper are the automatic identification of natural features, and the organization of these features as a visual graph, covering the whole path. The control of the vehicle is based on the visual servoing paradigm and it is performed by continuously and incrementally updating the vehicle's trajectory. The automatic selection of generic visual features of the scene is performed by a newly implemented multiresolution technique, based on morphological filtering and a “winner take all” strategy. Even though this technique allows to find any type of generic feature, in our implementation we restrict the analysis to corners, vertical lines and edge blobs (regions containing high density contours). The recognition of the features, which is a prerequisite for control application, is performed by multi-resolution correlation of the filtered images. The paper provides experimental evidence of the validity of the proposed approach. Detailed results are presented concerning the feature extraction procedure, the visual graph construction and the subsequent matching among similar features. Preliminary results concerning the navigation of a mobile robot along simple indoor paths are also presented.

In this paper, the problem of controlling the position of a robot camera with respect to an object is addressed by carefully choosing the system state representation and applying nonlinear control theory. The robot camera-object interaction model assumes an affine shape transformation in the image (weak perspective camera) thus reducing the size of visual representation according to active vision requirements. The proposed control law is proven to ensure global asymptotic stability in the Lyapunov sense, assuming exact model and state measurements. Robustness analysis is also carried out. The pose ambiguity arising from the use of linear models is solved at the control level by choosing an hybrid state vector including both image space (2-D)in formation and object 3-D parameters, which are all estimated on line without requiring camera calibration. Experimental results validate the theoretical framework both in terms of system convergence and control robustness.

In this paper we apply a wavelet-based controller to a hand-held mechatronic drill. The penetration velocity of the drill is generated on the basis of the wavelet analysis of the thrust force signal and the controller fulfils different tasks which correspond to different kinds of hole to be done through layers of different materials. The wavelet transform allows deep insight into the signal features, due to the analysis performed on the signal at different resolution levels (from which the term of “multiresolution analysis”), which allow to extract both the general trend of the analysed sequence and its details. Many studies have demonstrated the capability of WT analysis with the Haar basis of enhancing abrupt changes in the signal such as those arising at interfaces between layers of different materials. Moreover, the choiche of the Haar mother wavelet makes the computational effort low and suitable for real-time implementation. Results from real experimental data are presented and discussed.

This paper describes the design, development and future activities for the ongoing EU MAST I1 and I11 programmes AMADEUS I and II. AMADEUS is a programme of work focused on improving the dexterity and sensory abilities of underwater systems for grasping and manipulation of delicate and other objects. Phase I of the project was completed in May 1996, and has developed a prototype dextrous three fingered underwater dexterous gripper. Phase II is now underway, to deploy the hand from an underwater robot arm, and carry out wet trials with end users. This paper summarizes the major achievements obtained within the program.

Calculating smooth trajectories of bounded curvature has received a very wide attention in the robotic literature of the last 40 years. Most results focus on the study of wheeled non-holonomic vehicles and are concerned with 2D path generation algorithms. The problem of smooth and least curvature 3D path planning is addressed with a variational approach and the general 3D Euler-Poisson equation is derived. The 2D solution is calculated as the plane projection of the general 3D solution and some special 2D cases are analyzed. It is shown that if some special conditions are satisfied along the 2D path the optimal solution is approximated by the well known Cornu spiral; moreover in these same conditions the optimal solution (and the Cornu spiral) are approximated by the more familiar cubic polynomial. Applications to rigid body underwater dynamics are discussed.

A receding horizon control strategy for constrained linear systems based on continuous optimization of an infinite horizon quadratic performance cost is described. Input predictions are expressed as a finite-dimensional perturbation of an L²-stabilizing control law. Input and output constraints are characterized in terms of an admissible region in the system state space augmented by perturbation parameters, the boundary of which is an explicit function of prediction extremum points. An asymptotically optimal control law is then obtained by continuously adapting perturbation parameters on the basis of the cost gradient and asymptotically convergent estimates of prediction extrema. Closed-loop stability and convergence are guaranteed by the stability properties of predictions and the propagation of a guarantee of feasibility.

This paper presents design of P- and PD- controllers for the single and double integrator plant models with dead time and constrained input. The well known design procedure guaranteeing a double real closed loop pole used for tuning of the P-controller for a single integrator system with dead time is extended for the case of a double integrator with dead time controlled by a PD-controller. Its parameters are determined to guarantee a triple real closed loop pole. A new notion of equivalent poles is introduced to approximate the above design by the standard pole assignment controller, whereby recommendation for the choice of the closed loop poles in dependance on the dead time are proposed. The equivalent poles are substituted into the near to minimum time pole assignment controlled derived for the double integrator with constrained control signal without dead time. This procedure gives good results also in controlling constrained systems with dead time.

In this paper we consider a linear system subject to uncertain parameters varying in time with a bounded rate and ranging in a hyper-rectangle. As shown in previous papers, sufficient conditions for the exponential stability of the system can be obtained with the aid of parameter dependent Lyapunov functions. In this paper we propose a new approach to the search of parameter dependent Lyapunov functions which leads to much less conservative conditions for system stability at the price of a greater computational burden; this limits the application of the methodology to systems containing up to three parameters. The technique will be applied for testing robust stability versus bounded rate parameters of the control system designed in⁷ for the automatic steering of a bus.

A new model reduction technique for the approximation of balanced realization is introduced. The method consists in a further generalisation of the Generalised Singular Perturbation Approximation by adding several parameters that can be tuned according to a specified performance criterion. An a priori bound can be computed guaranteeing the quality of the approximated model in the whole range of parameters, variations. Two numerical examples conclude the paper

Two dynamical classes of anti-windup pole assignment controllers based on the single and double integrator plant models with dead time are presented. They may be considered as the minimum time controllers with additional restriction on the control signal (state) changes per sampling period specified by the closed loop poles. The linear pole assignment control as well as the “bang-bang” minimum time control are involved as limit cases. A special attention is devoted to the dead time compensation by a choice of the closed loop poles (passive compensation), by a generalized Smith's predictors (active compensation), or by a combination of the both above methods (mixed compensation). Both controllers may be extended by the “anti-windup” I-action. In difference to standard anti-windup techniques, no additional design parameters are introduced other as the closed loop or observer poles. A broad applicability of the tuning procedure based on the plant approximation by the I₁- and I₂- models with dead time is shown.

The problem addressed in this paper is the linearization of nonlinear systems by generalized input-output (I/O) injection in order to build observers with linear error dynamics. The I/O injection (called “completely generalized I/O injection”) depends on a finite number of time derivatives of input and output functions. The method is based on the study of the I/O differential equation structure. Thus, the problem is solved as a realization one. A necessary and sufficient condition is proposed through a constructive algorithm. This condition uses exterior differentiation and is fully constructive.

In this paper, we study the problem of stabilizing a nonlinear control system by means of gradient descent control algorithm which is a dynamic feedback control law. In this algorithm, we consider the equilibrium point as a desired value and define a performance index as a squared error function. Then by applying the direct gradient descent technique we design the dynamic control law to decrease the performance index most rapidly.

The input-output decoupling problem is studied for a class of recursive nonlinear systems (RNSs), i.e. for systems, modelled by recursive nonlinear input-output equations involving only a finite number of input values and a finite number of output values. The solution of the problem via regular static feedback known for discrete time nonlinear systems in state space form, is extended to RNSs. Necessary and sufficient conditions for local solvability of the problem are proposed.

This paper presents a remark on the differential algebraic description of analysis and synthesis problems for nonlinear systems. The description represents a more procedural view of the well established language of differential algebraic systems theory. The main result presented in this paper is a proposal for the investigation of differential algebraic rank conditions as well as for the synthesis of nonlinear state space feedbacks.

The problem of global tracking control with disturbance attenuation of general Euler Lagrange systems without velocity measurement is still unsolved so far. In this note, on the basis of some appropriate choice of state coordinates, a solution is proposed for a particular class of such Euler Lagrange systems. Results are illustrated on the academic example of an inverted pendulum on a cart.

In this paper we study the problem of semiglobally stabilizing uncertain nonlinear systems via measurement feedback, characterized by a nominal linear part and (measurable) uncertain nonlinear terms, which are known only up to some nonlinear bounds. Our result recovers and generalizes well-known results for the case of uncorrupted outputs and input saturations

Based on the system lower Hessenberg forms for single-input linear systems and a known method for the right coprime factorization of linear systems, a simple, efficient, iterative procedure for determining a right coprime factorization of a single-input linear system is proposed. The procedure uses numerically reliable techniques for finding the Hessenberg forms and involves only the production of a series of scalar polynomials with coefficients derived from products of the parameters of the system Hessenberg form.

New algorithms are proposed for triangularizing polynomial matrices over the field of polynomial fractions and over the ring of polynomials. They are based on Sylvester matrices. With contrast to already available triangularization methods, the algorithms described in this paper only rely upon efficient and numerically reliable routines. They can also be used for greatest common divisor extraction, polynomial rank evaluation or polynomial null-space computation.

The main purpose of this note is to present a quicker and less expensive in memory algorithm for the generalized inversion of polynomial matrices than the existing ones presented in Karampetakis (1997a, 1997b)‥

This paper presents an algorithm for the row reduction of nonsingular polynomial matrices. The algorithm is based on polynomial matrix to state space and vice versa conversions, avoids computation of elementary polynomial operations, and relies on well-proven methods of numerical linear algebra such as Householder transformations and Hessenberg forms

The purpose of this paper is to prove the minimum variance property of two 2D, recursive, finite-dimensional filters. The filtering algorithms are derived from general basic assumptions underlying the stochastic modelling of an image as a 2D gaussian random field. An appealing feature of the proposed algorithms is that the image pixels are estimated one at a time; this makes it possible to save computation time and memory requirement with respect to the filtering procedures based on strip processing.

The problem of identification of continuous-time plants has been treated with the application of three approaches, namely the least squares, approximate maximum likelihood and instrumental variable methodologies. The continuous-time system estimates are obtained based on a regression vector which contains consecutive multiple integrals of the input and output signals. The continuous-time algorithms and the continuous-time regression vector derived are transformed into the discrete-time domain by utilizing basic numerical integrating schemes. The discrete-time realizations of the continuous-time estimate are verified by simulation means.

This talk aims at providing a brief state-of-the-art and at pointing out some open problems in the field of modelling, analysis and control of finite-dimensional mechanical systems subject to unilateral constraints. Such systems belong to a class of hybrid dynamical systems since they contain both discrete-event (DE) and continuous dynamics. The DE part of the dynamics is a consequence of the complementary-slackness nature of such systems: the system may a priori evolve through a finite number of modes. The switching from one mode to another generally occurs via state-jumps, hence the inherent nonsmoothness of such hybrid systems. It is noteworthy that contrarily to many other hybrid systems considered in the literature whose hybridness is primiraly due to a switching input, those complementary-slackness dynamical systems possess a “natural” (or open-loop) hybridness. In this note we present and discuss some models and some problems (mechanics, mathematics, stability) which are associated to such systems.

In this paper, we show how neural networks can be used to implement extrapolative models of nonlinear dynamic systems. These extrapolative models are needed for generating the residual sequence which is then used for fault detection. The technique presented in this paper is applicable to deterministic or stochastic time-invariant nonlinear systems. Computer simulation results are presented in order to demonstrate the implementation. Once the residual sequence is generated, standard tests of hypothesis can be used for fault detection.

A recently introduced singular value-based fuzzy identification approach characterizes membership functions by the conditions of Sum Normalization (SN), Nan-Negativeness (NN), and, possibly, Normality (NO). In previous works, the NO condition was attempted over the full domains of the variables, and resulted in only a subset of the membership functions satisfying the condition. In this paper, a new procedure to applying the NO condition over subdomains of the full range is introduced. The procedure enables the possible incorporation of the NO condition to all membership functions. The price to pay is an increased number of membership functions for the realized system.

A new analytic approach to an adaptive Fuzzy Logic Control FLC) system synthesis without any fuzzy rule base is proposed. For this purpose, among the others, an optimal parameter β-adaptation algorithm for adaptation of FLC systems has been developed. A real capability of the proposed FLC synthesis procedures is presented by synthesis of an adaptive FLC system of robot of RRTR-structure.

This paper extends the work of [1] on the identification of fuzzy system. Instead of relying on the samples over a set of rectangular grid points for identification, the present approach uses a set of randomly scattered samples to approximate the grid point samples in a least square error sense, and then applies singular value decomposition (SVD) approach developed in [2] to the approximated samples. The resulting matrices from SVD are tailored to becoming the identified membership functions and rule consequents according to the conditions of Sum Normalization (SN), Non-Negativeness (NN), and Normality (NO). Product-sum-gravity inference emerges Naturally from the structure of the matrix equation. The output error at the sampling points now consists of the errors due to the grid point approximation and the SVD-based fuzzy identification. The present approach applies to fuzzy systems with a general number of antecedent variables. A numerical examples is included to illustrate the effectiveness of the approach.

In this paper, a method is proposed to identify the magnetization function of switched reluctance motors using fuzzy techniques. A general procedure for the identification of this function based on a set of voltage and current measurements has been implemented. Such a procedure can be applied for the reconstruction of the magnetization characteristic of a wide class of switched reluctance machines. The method allows to build up an approximating fuzzy system based on a FAM (fizzy Associative Memory) bank, starting from a set of numerical samples. The FAM bank can be trained either keeping the rotor locked in a set of previously chosen angular positions or during free motor revolution. The second approach is directly suitable for on line application and does not require the use of an ad hoc experimental testbed.

The performance analysis and optimization of manufacturing systems modeled as timed event graphs (TEG'_s) is the focus of this paper. The choice of such modeling tool is due to the possibility of exploiting some simple results related to TEG'_s and revelent to the steady sate behavior of the system the class manufacturing systems considered is characterized by the presence of a material handling system made up of a set of AGVs in this framework the optimization problem dealing with the maximization of the system productivity while minimizing the cost of both the material handling system and the work in progress is formalized being the decision variables the lit size the number of AGV's to be used in the production plant their pickup and delivery sequences and the work in progress A procedure is developed to optimize sequentially such performance indices.

The control of a discrete event dynamic system (DEDS) can be often posed as the optimization of a performance index defined on it. An analytical expression for this performance index is usually not available and its value is known only through noisy estimates. Many algorithms have been presented to solve this problem in the stationary case. This paper deals with non-stationary DEDS the performance index is a time-varying function. In this paper a new algorithm is presented which solves the considered problem. Simulation experiments considering a multi-part type kanban-based manufacturing system show the effectiveness of the proposed scheme.

For finite-buffer automated manufacturing systems, the major stability issue is deadlock rather than bounded-buffer stability. In this paper, for a class of finite-buffer multiple reentrant flowline systems, necessary and sufficient conditions are given for the absence of deadlock. This leads to a multiple part-type last-buffer-first-serve dispatching policy that not only guarantees deadlock-free operation but also allows an efficient utilization of the resources. Petri net (PN) techniques are used in the analysis, introducing the notion of ‘critical siphon’, as well as the new notion of ‘critical trap’. The problem of computational complexity is overcome by using certain submatrices of the PN incidence matrix, based on which computationally efficient matrix techniques are given for implementing the proposed dispatching policy.

Sequential Functional Charts (SFCs, also known as GRAFCETs) have proven themselves to be effective tools for modeling and control of manufacturing systems. SFCs are similar to Petri nets in that they are composed of steps, transitions and directed arcs; similar transition rules also apply but in SFCs the marking of the steps is strictly boolean, simultaneously fireable transitions are simultaneously fired, conditions may depend on the state of the marking.

The use of hierarchical SFCs, i.e. when some SFCs can directly modify the marking of other SFCs, improve their modeling capabilities and solve some very important problems in the design of control algorithms. A typical example is the handling of alarm conditions where it is necessary to be able to suspend the evolution of the control algorithms or to drive the system into a safe state. Hierarchy of SFCs can be accomplished by resorting to the macro-actions concept.

If SFCs are to be converted into executable code on standard Programmable Logic Controller a conversion method has to be devised that is consistent with the evolution rules. In this paper a conversion method is proposed that implements the evolution algorithm without stability search. The method produces a unique executable program starting from a set of SFCs, eventually hierarchical. A case study about application of SFCs to the control of a material handling system in a pharmaceutical manufacturing plant is also presented. The advantages of using SFC in all the phases of the software development cycle (design, coding, testing and documenting) are discussed.

In this paper we consider sequences of consecutive powers of boolean matrices in the max-plus algebra, which is one of the frameworks that can be used to model certain classes of discrete event systems. The ultimate behavior of a sequence of consecutive max-plus algebraic powers of a boolean matrix is cyclic. First we derive upper bounds for the length of the cycles as a function of the size of the matrix. Then we study the transient part of the sequence of consecutive powers of a max-plus-algebraic boolean matrix, and we derive upper bounds for the length of this transient part. These results can then be used in the max-plus-algebraic system theory for discrete event systems.

This paper contains three main results. Firstly, a complete solution of the Linear Non-Homogeneous Matrix Differential Equation (LNHMDE) is presented that takes into account both the non-zero initial conditions of the pseudo state and the non-zero initial conditions of the input. Secondly, in order to characterise the dynamics of the LNHMDEs correctly, some important state space concepts such as the state, slow state (smooth state) and fast state (impulsive state) are generalized to the LNHMDE case and by these means the solution of the LNHMDE is separated into the smooth (slow) response and the fast (implusive) response. Finally a new characterization of the impulsive free initial conditions of the LNHMDE is given.

By using some of the properties of non-negative irreducible matrices, some convex subsets of the Schur stability domain of polynomials in the parameter space are presented, which are maximal in some senses and may have applications in robustness analysis and design. As an application an efficient method for the stabilisation of discrete SISO interval systems is proposed. An example is presented which demonstrates the effect of the method.

This paper is concerned with eigenstructure assignment with mixed performance specifications for multivariable systems. It combines time-domain performance specifications provided by eigenstructure assignment and robust performance specifications in the frequency domain considered by H_∞ control to realize joint optimal robust control design. A parametric expression for state-feedback eigenstructure assignment is derived on the basis of a set of free parameters. The mixed performance function is a combination of the robustness index defined in the frequency domain and the desired eigenvector assignment in the time domain. The optimal controller design is discussed by making full use of the freedom provided by eigenstructure assignment.

This paper details a mathematical procedure for the modelling and simulation of distributed-lumped parameter systems. This procedure can readily be implemented using CAD packages such as MATLAB and is computationally efficient, when compared to the alternative solution of a fully distributed system. The paper considers two practical engineering examples in which the system are considered as partially lumped and partially distributed. The System admittance matrix is derived and simulation modules that can be used in MATLAB Simulink are presented.

The problem of global temperature control for a general class of chemical reactors is addressed and solved using Lyapunov techniques. The proposed results improve recent published works. Moreover the mathematical model considered is more general than the one examined in previous papers, as it also takes into account the jacket dynamics. As a result, the temperature subsystem has relative degree two and not one. Therefore, the stability study is much more involved and cannot be performed with simple tools. The main result of the paper shows that, under reasonable and easy to test assumptions, global temperature control can be achieved with bounded output feedback control. The control bounds can be very general and tight, and the only condition to be fulfilled is a simple and natural feasibility condition, namely that the steady state control is admissible. The theory is illustrated on a simple simulation example.

The concept of componentwise stability for discrete time systems is extended to cover the situation where the number of components in the state vector can change with time, so that it becomes applicable to the wave advance model, which is a one-dimensional representation of a multidimensional system. A more concise formulation of the conditions for component wise exponential asymptotic stability is also given, and some illustrative examples are presented.

This paper considers the problem of designing near-optimal finite-dimensional sampled-data controllers for single-input single-output (SISO) and possibly unstable distributed parameter plants. A weighted ℋ^∞-style mixed-sensitivity measure which penalises the control is used to define the notion of optimality. Controllers are generated by solving a “natural” finite-dimensional sampled-data optimisation. Condition are given on the approximants such that the resulting finite-dimensional controllers stabilise the sampled data controlled distributed parameter plant and are near-optimal. The proof relies on the fact that the control input is appropriately penalised in the optimisation. This technique also assumes and exploits the fact that the plant coprime factors can be approximated uniformly by finite-dimensional systems. Moreover, it is shown how the optimal performance may be estimated to any desired degree of accuracy by solving a single finite-dimensional problem using a suitable finite-dimensional approximant. The proofs and constructions given are simple. Finally, it should be noted that no infinite-dimensional spectral factorisations are required. In short, the paper provides a straight forward control design approach for a large class of SISO and possibly unstable distributed parameter systems under sampled-data control.

The purpose of this note is to investigate the existence of solutions to a class of second order distributed parameter system with sudden changes in the input term. The class of distributed parameter system under study is often encountered in flexible structures and structure-fluid interaction systems that use smart actuators. A failure in the actuator is modeled is either an abrupt or incipient change of the actuator map whose magnitude is a function of the measurable output. A Galerkin-based finite approximation for the adaptive diagnostic observer and its on-line approximator is proposed in order to facilitate the numerical implementation of the aforementioned diagnostic observer.

In this paper we address the parameter estimation problem of a discrete-time, partially observed Gauss-Markov linear system. We use conditional moment generating functions to yield filtered estimates of the functionals required to obtain Maximum Likelihood (ML) estimates via the Expectation Maximization (EM) algorithm. Each functional is estimated by a bank of Kalman filters consisting of four statistics; two are the Kalman filter statistics while the remaining two are given by a Kalman filter type equations driven by the innovations of the former Kalman filter. The EM algorithm uses a bank of these filters to yield ML parameter estimates of Gaussian state space models.

This paper presents control laws for DPS of parabolic type which do not utilize second spatial derivatives of plant output and permit on-line plant parameter estimation. The main feature of the proposed MRAC laws is in the use of auxiliary systems, the time-varying parameters of which admit simultaneous convergence to their nominal space-varying values when appropriate input signals in reference models are used. The class of sufficiently rich input signals referred to as generators of persistent excitation is defined. This class guarantees the existence of a unique steady state for the parameter errors, thereby yielding unknown plant parameters. The development a MRAC control law with the same properties for hyperbolic systems has also been carried out but is omitted due to space limitations.

In this paper we present a new approach for the modeling and control of flexible manufacturing systems (FMS) characterized by unreliable machines, buffers of finite capacity, arbitrary service time distributions and deterministic sequencing and routing policies. Our main goal is the design of the FMS configuration embedded with its optimum control policy. The problem is addressed using first and second order fluid approximation obtained by splitting the process in two hierarchical layers and defining what we call micro and macro events. With an original approach this fluid approximation lends itself to a discrete time linear stochastic state variable model which offers average values and variances of both performance measures and of their gradients with respect to the most significant FMS parameters. Finally we investigate problems concerning the non-differentiability of the performance indices with respect to certain design parameters, specifically the control parameters as they appear as structural elements of the model.

A general hierarchical control framework is considered in order to support the integrated planning and scheduling of manufacturing systems. These may be viewed as complex discrete event dynamical systems whose state evolution, governed by several decision layers, occurs in different time scales and is affected by both undesirable perturbations as well as by relevant interactions with other independent external systems with which it shares segments of the supply chain. Motivated by the analysis of two different classes of production systems having in mind the respective integrated planning and scheduling, this approach is supported in a properly adapted Systems Engineering Process in order to capture all the relevant ingredients underlying the decision-making at all levels of the hierarchy. It is recognized the role of the optimal control framework at the coordination level as well as in providing the interface to the supply chain integration level. While in the first one, complexity and random factors are dealt with by embedding the basic problem into a receding horizon scheme, in the second level, a Hybrid Systems framework plays a fundamental role in enlarging the scope of decision-making which now encompasses system's reconfigurability.

The article presents a synthetic overview of a mathematical framework for the analysis of discrete manufacturing systems in view of their hierarchical real-time production control. The framework is based on a recently developed mathematics, called Manufacturing Algebra (MA). defining in an axiomatic way the six elements (objects, MO, PU, RU, SU and CU) to be used for assembling the dynamic models and the hierarchical control systems of real production processes. The dynamic models are defined as discrete-event operators with their own state-equations. The MA elements can be composed to create aggregated entities keeping the same input-output and dynamic properties of the basic elements and therefore suited for hierarchical control design. Specifically, the aggregation methodology allows to bottom-up simplify the discrete-event dynamics in order to create a hierarchy of event ensembles, each feeding or being created by the appropriate decision level.

In this paper, a new methodology is introduced to approximatively solve combinatorial problems arising particularly in discrete event systems. This methodology consists in first modeling the problem into dynamic programming in the strict sense. When a problem is combinatorial the number of states in the dynamic programming formulation increases exponentially with the size of the problem. In order to reduce the complexity, states are aggregated. This gives rise to the notion of “aggregated states”. The aggregation is done in such a way that the number of aggregated states is a polynomial or pseudopolynomial function of the size of the problem and transitions exist between states. So doing, the optimality is naturally lost. The interesting point of this mathodology is that comparaed with classical step-by-step construction approximation methods, this approach preserves a global view of the problem.

This paper discusses the problem of controlling a Petri net whose marking cannot be measured. An observer is used to estimate the actual marking of the plant based on partial information of the initial marking and on event observation. This estimate is used to design a state feedback controller, that ensures that the plant in closed-loop evolves through a set of legal states. We present an efficient algorithm, that generalizes previous results, to design a safe observer-controller for legal states defined by linear constraint sets.

In the last few years, different robot systems with multifingered grippers have been developed and a lot of research has been done in the field of grasping and manipulating objects with such grippers. With the help of fingers it is possible to grasp different objects with different shapes like the human hand without changing the gripper. As a multifingered gripper has normally at least three fingers and each finger at least three degrees of freedom, grasped objects can be moved between the finger tips in any direction. Performing such fine motions puts high demands on the hard - and software. The hardware can be seen as the base of a robot system including the mechanical system, sensors, actuators and a control computer. On top of this base, a suitable control system is placed. This paper gives an overview on the hard- and software of the new Karlsruhe Dextrous Hand II and describes in particular one part of the sensor system: the object state sensors.

A survey is made of automated handing systems for the assembly of limp materials concentrating on those applicable to the garment and shoe industries. Reliability is highlighted as a major issue and it is shown how environmental changes can have an important effect on the material properties and hence the behaviour of the automated systems. This knowledge, combined with analyses of automated handling processes will be used in the future to make more reliable automated handing systems for industry and the home.

The control of internal forces is paramount in robotics grasping. In force closure grasps internal forces can be controlled in order to prevent the object from possible slippage due to external disturbances. A cost function approach to compute the internal force is proposed. The cost function weights the distance of the contact force from the friction constraints and from the maximum and minimum force levels allowable in the system. A globally asymptotically convergent algorithm returns the optimal internal grasp forces which will be used as the reference of a force control loop.

This article presents an impedance control strategy for grasping tasks. The presented idea is based on what is called the “Virtual Object Concept” and can be used both for tips and full grasps. Some short considerations will also be done for tip rolling contacts. One of the major advantages of the presented strategy is the passive nature of the algorithm and the physical intuition which ensures stability in all the situations included the transition from no contact to contact and vice versa.

The paper outlines DLR's new 4-finger hand characterized by the fact that all 12 active joints (3 for each finger) are integrated into the fingers or the palm. With 112 sensors, around 1000 mechanical and around 1500 electrical components the new hand is one of the most complex robot hands ever built. Its key element is the ,,artificial muscle ®“ a small but powerful linear actuator, which seems to be one of the first real electromechanical alternatives to hydraulic or pneumatic actuators.

Manufacturing shop-floor control is concerned with sending on-line timely orders to work stations to perform the required operations with respect to a given manufacturing plan and subject to the current shop-floor status. Reactive shop-floor control is concerned with real-time control in the case of unexpected events, be they endogenous (machine breakdowns, empty stocks etc.) or exogenous (unplanned orders, order priority changes etc.). In this paper, we compare two control architectures for discrete manufacturing based on multi-agent systems that have been developed at LGIPM, Metz for reactive shop-floor control. One is a strictly hierarchically decentralised architecture based on two types of non negotiating agents (cognitive agents and reactive agents) while the other one is a fully distributed architecture involving negotiating expert agents. While the hierarchical architecture has been proved to have very fast response times and can easily be adapted to a wide variety of manufacturing systems, the fully distributed architecture is more flexible and can potentially handle a wider range of exceptional situations (depending on the degree of intelligence of its agents) but at the expense of lower response times and increased complexity of the system.

In this paper the Group Technology problem of grouping parts in families and machines in cells in order to convert a job shop production system to some pseudo flow shop is considered. Several heuristic methods for solving Group Technology problem have been proposed in the literature, in general, not producing a flow shop in each cell—unless a great number of extra machines is added. We use known techniques for solving the Shortest Common Super sequence and the Longest Common Subsequence problems to develop a method that takes into account the sequence of machines that each part has to visit. This new method allows us to obtain a flow shop layout for the machine cells using a limited number of machines in each cell.

We consider the problem of assigning parts and tools on a Flexible Manufacturing System composed by W identical parallel workstations, so that the workload of the workstations is well balanced. The goal is to minimize the total number of tools needed on all workstations, including multiple copies, if any. We give an integer programming formulation of this problem and a strong cutting plane algorithm to solve it. We used cover inequalities for the 0–1 knapsack constraints and other valid inequalities to strengthen the formulation and applied branch and cut method. Computational experiences on some real world problems and randomly generated problems are reported.

A formal framework is presented to specify and analyse the behaviour of discrete manufacturing systems in terms of processes and agents, where process behaviour is specified using a declarative workflow language based on a process algebra and agent behaviour is specified by means of state-charts. The link between processes and agents is materialised by elementary actions, called functional operations. The proposed framework can be used to specify the structure of manufacturing systems and to analyse and simulate their behaviour.

A cook must prepare n cakes using an oven with m < n racks. According to the recipe, the i-th cake has to be cooked for exactly a_i minutes. Cakes to cook are taken from a table and carried to the oven, and once cooked are carried back to the table. To this aim, the cook is provided with a trolley with the same capacity (in terms of cakes) as the oven. What is the minimum number q* of round trips required of the cook? We show i) that the problem of computing q* is at least as difficult as that of factorizing an m-regular graph into perfect matchings; ii) that however, for m = 2, active schedules with q* trips always exist; iii) that the problem significantly simplifies if the cook accepts to stay near the oven for a while (not much, indeed). Finally, we propose a column generation method to solve at optimality problems with 2 racks and up to 100 cakes.

In this paper several new methods are proposed to find feedback matrices such that all the eigenvalues closed-loop lie in a specified sector or vertical strip. These methods use from the properties of the real and complex Riccati equation yielding straight forward algorithms. In particular using the real Riccati equation with zero right-hand side yields all the eigenvalues in the specified sector. We improve the eigenvalue placement in previous work and present a method to yield all the eigenvalues of the closed-loop system in a specified vertical strip in the left-hand half-plane without necessary assumptions on the eigenvalues of the state matrix of the system.

The problem of obtaining a continuous-time (i.e.ripple-free) input-output decoupled system for a continuous-time linear time-invariant plant, by means of a purely discrete-time compensator, is stated and solved in the case of a unity feedback control system. Such a control system is hybrid (since the plant is continuous-time and the compensator is discrete-time) and periodic, since the samplers and the holders are periodic. A necessary and sufficient condition for the existence of a solution of such a problem is given, which reduces the mentioned hybrid control problem to an equivalent purely continuous-time decoupling problem. A simple necessary and sufficient condition for the existence of a solution of such a continuous-time decoupling problem is given for square plants (with and without the additional requirement of the asymptotic stability of the over-all control system), together with a parameterisation of all the decoupling controllers. Moreover, for square plants, it is shown that, whenever the hybrid control problem admits a solution, any solution of the corresponding decoupling problem for the discrete-time model of the given continuous-time system is also a solution of the hybrid control problem.

For linear periodic discrete time systems the analysis of the model error introduced by a truncation on the balanced minimal realization is performed, and a bound for the infinity norm of the model error is introduced. The results represent an extension to the periodic systems of the well known results on the balanced truncation for time-invariant systems. The general case of periodically time-varying state-space dimension has been considered.

The following sections are included:

• AUTHOR INDEX