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This paper presents a tracking control strategy for a class of chaotic systems. A general tracking controller is designed. It is proved theoretically that the error signal can exponentially converge to zero. Numerical simulations show that the controller can make the output signal track all kinds of reference signals. Besides, a better effect can be obtained via changing the control parameters properly.

In this paper, a new hyperchaotic system is formulated by introducing an additional state into the third-order unified system. Some of its basic dynamical properties, such as Lyapunov exponent, bifurcation diagram and the Poincáre section are investigated. It was found that the system is hyperchaotic in several different regions of the parameters. The analysis of equilibrium points and stability are also given. Two different methods, i.e., nonlinear hyperbolic function feedback control and tracking control methods, are used to control hyperchaos in the new hyperchaotic system. Based on the Routh–Hurwitz criteria, the conditions suppressing hyperchaos to unstable equilibrium point are discussed. A tracking control method is proposed. It is also proved that the strategy can make the system approach any desired smooth orbit at an exponential rate. Numerical results have shown the effectiveness of the control methods.

This paper presents tracking control and synchronization strategies for Chen system. Two universal controllers, a tracking controller and a synchronization controller based on Backstepping design method were designed. It is proved theoretically that the tracking controller enables the error signal exponentially to converge to zero. The validity of Backstepping synchronization controller is also proved. Numerical simulations further validated the two controllers.

In this paper, the six degrees of freedom adaptive tracking control for chaser spacecraft with uncertainty and disturbance to approach a noncooperative target are studied. The system equations with coupled relative translation and relative rotation are modeled. Considering the unknown inertia uncertainties and state-dependant disturbances, a backstepping-based adaptive tracking control law is developed to achieve high-precision proximity operations between chaser and noncooperative target. The unknown inertia and disturbance are estimated by adaptive update laws. The properties of the developed control law are discussed through the comparison of simulation results.

In this paper we study the tracking control of Lagrangian systems subject to frictionless unilateral constraints. The stability analysis incorporates the hybrid and nonsmooth dynamical feature of the overall system. The difference between tracking control for unconstrained systems and unilaterally constrained ones, is explained in terms of closed-loop desired trajectories and control signals. This work provides details on the conditions of existence of controllers which guarantee stability. It is shown that the design of a suitable transition phase desired trajectory, is a crucial step. Some simulation results provide information on the robustness aspects. Finally the extension towards the case of multiple impacts, is considered.

Fast tracking is one of the most important performance indices in servo systems. To ensure fast tracking performance, many design methodologies have been established. This note proposes yet another new method based on the idea of intended instability. This is essentially a framework within which a variety of design approaches can be developed. Specifically, fast tracking through slow switching, fast switching, as well as compound control is explained. Refinement of the design approaches is also brought up. Numerical simulations are performed for the illustration of the corresponding designs.

In this study, we develop a novel multi-posture lower limb rehabilitation robot with three postures, which can provide different amplitudes and frequencies of rehabilitation training for hip, knee and ankle joints, respectively. The kinematic and dynamic analyses of the robot are carried out to solve the kinematic forward and backward solutions and the Lagrangian dynamics equations of the lower limbs. The angle, angular velocity and angular acceleration ideal trajectory curves of the rehabilitation motion are derived by using a quintic polynomial trajectory planning scheme. An improved ions motion optimization (IIMO) algorithm is proposed and applied to optimize the initial weight of back propagation (BP) neural network, and algorithm is used to adjust five parameters of fractional order ${\mathrm{\text{PI}}}^{\lambda }{\mathrm{\text{D}}}^{\mu }$ (${\mathrm{\text{FOPI}}}^{\lambda }{\mathrm{\text{D}}}^{\mu }$) control in controller design. The passive training experiment results of prototype show that the designed controller has the largest average error of angle and angular velocity of hip, knee and ankle joints in high amplitude and high frequency movement mode, which are 1.091^∘, 0.716^∘, 0.412^∘, 1.551^∘/s, 1.394^∘/s, 1.498^∘/s, respectively. At low amplitude and low frequency, the maximum average errors are the smallest, which are 0.351^∘, 0.341^∘, 0.167^∘; 0.833^∘/s, 0.842^∘/s, 0.398^∘/s, respectively. The actual trajectory curve fits well with the designed one. The highest accuracy of angle and angular velocity can reach 99.165% and 99.116% through comprehensive comparison of all motion modes. Therefore, the overall error is small. The stability of rehabilitation training process is ensured, and the rationality and effectiveness of trajectory planning and control design are verified.

In this paper, a design method of optimal tracking control based on finite-time stability for quadratic performance index is proposed. Finite-time stability of tracking control involves dynamical systems whose actual output can track desired output in finite time while satisfying Lyapunov stability. A nonlinear control law which guaranteed finite-time stability is designed depending on the core idea of dynamic programming. By using Hamilton–Jacobi–Bellman (HJB) equation and finite-time stability theory, sufficient conditions involving V-function are provided, and design steps for nonlinear finite-time tracking control law are derived by constructing augmented systems. In addition, the V-function is constructed to obtain corresponding law for given systems, which verified that the design method is feasible. Simulation examples validate the efficiency of the results.

In this paper, the problems of chaos and chaos control for a class of susceptible-infected-removed (SIR) epidemic model with seasonal fluctuation are investigated. The seasonality in outbreak is natural among infectious diseases, as the common influenza, A type H1N1 influenza and so on. It is shown that there exist chaotic phenomena in the epidemic model. Furthermore, the tracking control method is used to control chaotic motions in the epidemic model. A feedback controller is designed to achieve tracking of an ideal output. Thus, the density of infected individuals can converge to zero, in other words, the disease can be disappeared. Finally, numerical simulations illustrate that the controller is effective.

This paper investigates the velocity and altitude tracking control problem for air-breathing hypersonic vehicle (AHV) in the presence of external disturbances and parameter uncertainties. A composite controller containing improved lines cluster approaching mode control (LCAMC) and nonlinear disturbance observer (NDO) is developed to guarantee the tracking errors converge to zero and enhance the robustness of control system. Meanwhile, considering the multiple uncertain parameters, a genetic algorithm (GA) based Pareto uncertainty estimation is employed to predict the parameter uncertainties of the AHV dynamics. Besides, the mathematical proofs of proposed method are analyzed by utilizing Lyapunov theory. Simulation results demonstrate the effective tracking performance, excellent disturbance estimation and uncertainty estimation ability of the composite method.

Machine learning-based data-driven approaches have greatly improved system identification capabilities and facilitated the application of model-based control algorithms. However, techniques such as neural networks require significant amounts of training data and have limited generalization capabilities. To overcome this problem, we employ the sparse identification of nonlinear dynamics with control (SINDYc) for system identification, which considers both system states and control inputs. Based on the identified system, we design the controller using the backstepping control method. In order to make the algorithm more practical in real-world scenarios, we introduce an input saturation compensation system into the controller design. Additionally, we apply a command filter into the method to avoid deriving a virtual control signal and reduce the computational complexity of the controller. Through stability analysis, the proposed control algorithm ensures that the tracking error in the system is bounded. Finally, we verify the effectiveness of the proposed SINDYc-Backstepping framework by conducting simulations using a single-link robot arm.

Feedback linearization methods are well known techniques for the control of nonlinear systems. Among them, the input-output feedback linearization method is input-output map is linearized by changing variables of the systems and using nonlinear feedback constructed by structure theories of the systems. A partial linearization method, which sets arbitrary state variable of systems as output of systems and sub-systems concerned in this state are partially linearized by input-output feedback linearization method, is widely applied to the control of underactuated systems. In general method, the linearized subsystems can track a constant reference value by a PD controller which is included in a nonlinear feedback. However, the PD controller is not guaranteed for tracking control of the time-variant reference function. In this paper, the new partial linearization method that guarantees that the linearized sub-systems track the time-variant reference function is proposed. The proposed method is based on a Lyapunov theorem and back-stepping control method. Numerical simulations are given to show the effectiveness of the proposed method.

The global population aging is increasingly serious and patients with lower-limb dysfunction caused by various diseases, injuries and traffic accidents have increased significantly. Motion control of lower limbs rehabilitation robot plays an important role. This paper deals with the tracking control of an omnidirectional lower limbs rehabilitation robot. The main research contents of this paper consist of two parts: 1) the kinematic and dynamic model is integrated within the control framework. 2) A PD control scheme is used to achieve the desired trajectories. Simulation tests are performed and demonstrate the feasibility and efficacy of the proposed method.

As key component of pointing and tracking mission of satellite, gimbal with two or more degree of freedom is usually mounted on the satellite in order to fulfill certain space mission, such as optical communication between satellites, target recognition, antenna with certain pointing direction and so on. In these missions, gimbal is mostly used to point to and track a space target or a given track. However, for most control method, because of their constant feedback parameter, the gimbal still track target with constant speed when the target is in high-speed or the satellite mounted with gimbal is suddenly undertaken shock. In fact, the gimbal could track target with different speed to improve pointing accuracy under particular circumstance. In order to solve the problem, an algorithm to revise feedback parameter is designed to be different functions of pointing angle error of gimbal. At last a simulation is carried out to verify the improvement of joint angle error using this algorithm under particular circumstance. The results proved that the joint angle error is efficiently decreased with feedback parameter revision.