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During worldwide epidemic of COVID-1, people started to depend on social media apps to cure their boredom. It was beneficial to provide information easily to a wide audience. The increased time people spent on their phones led to many, including teenagers and children, becoming addicted to social media, particularly TikTok. As a result, this usage of TikTok became an epidemic itself. Therefore, in this work, a fractional mathematical model is being developed to analyze the influence of TikTok on human population of different ages. In this paper, two equilibrium points for this model will be discussed and the theoretical stability will be proven. For numerical analysis, fractional Euler’s method will be used and the results will be discussed graphically and which group of population will be affected the most by frequent use of TikTok.

In this paper a nonholonomic mobile robot with completely unknown dynamics is discussed. A mathematical model has been considered and an efficient neural network is developed, which ensures guaranteed tracking performance leading to stability of the system. The neural network assumes a single layer structure, by taking advantage of the robot regressor dynamics that expresses the highly nonlinear robot dynamics in a linear form in terms of the known and unknown robot dynamic parameters. No assumptions relating to the boundedness is placed on the unmodeled disturbances. It is capable of generating real-time smooth and continuous velocity control signals that drive the mobile robot to follow the desired trajectories. The proposed approach resolves speed jump problem existing in some previous tracking controllers. Further, this neural network does not require offline training procedures. Lyapunov theory has been used to prove system stability. The practicality and effectiveness of the proposed tracking controller are demonstrated by simulation and comparison results.

In this paper we study the parallel solution of the discrete-time Lyapunov equation. Two parallel fine and medium grain algorithms for solving dense and large order equations on a shared memory multiprocessor are presented. They are based on Hammarling’s method and directly obtain the Cholesky factor of the solution. The parallel algorithms work following an antidiagonal wavefront. In order to improve the performance, column-block-oriented and wrap-around algorithms are used. Finally, combined fine and medium grain parallel algorithms are presented.

In reality, the types of vehicles running on the road and the driving experience of different drivers are probably different. Thus, the maximum velocity of each vehicle is usually different. Moreover, common driving experience indicates that drivers not only pay attention to the motion status of individual preceding vehicle in their view. With that in mind, an extended car-following model accounting for two preceding vehicles with mixed maximum velocity is constructed in this study. For analyzing the traffic flow’s evolution more accurately, theoretical and numerical analyses are conducted. In theoretical analysis, the model’s stability condition is inferred by using the control theory, and the mKdV equation is also derived to depict the propagation of traffic density wave by means of nonlinear analysis. Numerical experiments are performed to verify the correctness of theoretical analysis and to make a detailed analysis concerning the influences of factors considered on traffic flow. Theoretical and experimental results indicate that increasing the higher maximum velocity and the appearing probability of a car having higher maximum velocity is not conducive to traffic flow stability, and compared to only considering individual preceding vehicle’s motion status, it is obvious that the traffic flow with mixed maximum velocity is more stable when two preceding vehicles’ motion status is considered.

In this paper we prove the general result that, given a linear system where A is hyperbolic, u is piecewise linear and L-periodic, with , then there exists a unique L-periodic solution x = x_p(t) such that . We then consider a DC/DC buck (step-down) converter controlled by the ZAD (zero-average dynamics) strategy. The ZAD strategy sets the duty cycle, d (the length of time the input voltage is applied across an inductance), by ensuring that, on average, a function of the state variables is always zero. The two control parameters are v_ref, a reference voltage that the circuit is required to follow, and k_s, a time constant which controls the approach to the zero average. We show how to calculate d exactly for a periodic system response, without knowledge of the state space solutions. In particular, we show that for a T-periodic response d is independent of k_s. We calculate period doubling and corner collision bifurcations, the latter occurring when the duty cycle saturates and is unable to switch. We also show the presence of a codimension two nonsmooth bifurcation in this system when a corner collision bifurcation and a saddle node bifurcation collide.

Dynamical systems play a central role in the design of symmetric cryptosystems. Their use has been widely investigated both in "chaos-based" private communications and in stream ciphers over finite fields. In the former case, they take the form of automata named Moore or Mealy machines. The main charateristic of stream ciphers lies in that they require synchronization of complex sequences generated by the dynamical systems involved both at the transmitter and the receiver ends. In this paper, we focus on a special class of symmetric ciphers, namely the Self-Synchronizing Stream Ciphers. Indeed, such ciphers have not been seriously explored so far although they show interesting properties of synchronization which could make them very appealing in practice. We review and compare different design approaches which have been proposed in the open literature, and fully-specified algorithms are detailed for illustration purposes. Open issues related to the validation and the implementation of Self-Synchronizing Stream Ciphers are developed. We highlight the reason why some concepts borrowed from control theory appear to be useful to this end.

This paper first provides an introduction to the mathematical approach to the modeling, qualitative analysis, and simulation of large systems of living entities, specifically self-propelled particles. Subsequently, a presentation of the papers published in this special issue follows. Finally, a critical analysis of the overall contents of the issue is proposed, thus leading to define some challenging research perspectives.

Metabolic Control Analyses have led to significant advances in understanding the control of cell metabolism. However, the classical theory does not address all complex cases of the organization of cellular metabolism. Here the control theory is extended to include (i) pathways with high enzyme concentrations and moiety conservation and (ii) metabolic channelling in general. The new theory descends the microlevel of elemental steps into the reaction cycle of the enzymes and turns back to the macrolevel of complete enzyme reactions. We showed how the elemental control coefficients are related to the traditional flux control coefficients of the enzymes. We derived what the sums of the enzyme control coefficients are equal to in various non-ideal cell pathways.

In this paper, a fuzzy sliding mode controller (FSMC), which is synthesized by a collection of linguistic control rules whose membership functions of THEN-part is adapted, is proposed. Both the membership functions of IF-part and THEN-part are arranged symmetrically and distributed equally in the individual universe of discourse. In particular, the membership functions of the THEN-part can be adapted via one parameter adaptation to meet the required system specification. The proposed direct adaptive FSMC can be synthesized through the following stages. First, the control rules are constructed according to the concepts of SMC, and the fuzzy sets whose membership functions are symmetrically covered in state space. Then, the derived adaptive law is used to adjust the membership functions of the THEN-part. The FSMC is employed to approximate the equivalent control of SMC without knowing the mathematical model of the controlled system. Third, a hitting control is developed to guarantee the stability of the control system. Finally, we apply this FSMC to control a nonlinear inverted pendulum system for confirming the validity of the proposed approach.

Modeling and control of dimensional quality is one of deciding factors in current manufacturing competitions, and has always presented a great challenge to both scientists and engineers since for a multi-station machining system, the final product variation is an accumulation from all stations, and the complex non-linear relationship exits between dimensional quality and machining errors. This paper develops a linear state space model using homogeneous transformation to capture the influence of machined errors on dimensional quality, and the explicit expressions for system matrices of the model are explored. The proposed model employs a linear state space form, facilitating the use of the achievements of control theory, information technology and system engineering theory to support engineers supervisory control of physical machining processes, and it also can be used as an analytical engineering tool for efficient and effective faults diagnosis, system plan and design, and optimal sensors allocation. A real machining case illustrates the proposed model.

Technological advancements have affected each and every aspect of our day to day life. Over the last few decades our dependence on software products has increased immensely. At the same time, software technologies have been advancing at an electrifying pace to achieve new milestones. With this rapid development, competition between the developers is gaining new heights. In such a competitive business arena, customer satisfaction plays a vital role to decide on the survival of product in the market. So, it becomes essential for the firms to work on strategies of product portfolios to attract more customers in order to elevate profit levels. In this regard, firms are using different strategies to obtain a significant market share. An appropriate price becomes one of the most effective factors to influence customers demand. On the other hand, warranty length also acts as an attribute of quality and forms another factor that may sway the customer towards or away from the product. In a warranty contract, the seller or manufacturer promises for a free repair or renewal policy for failed products. In this paper, we have investigated the marketing and production problem for a software firm considering price and warranty as simultaneous dynamic decision variables under the condition of a dynamic demand. We have considered a demand function dependent upon price, warranty and cumulative sales. We have used optimal control theoretic approach for the proposed profit maximization model to derive optimal price and warranty policies. The results specify several optimal policies with which decision makers would gain insight into the consequence of their decisions. Further, genetic algorithm is used to find the optimal results. Numerical example is provided to illustrate the applicability of model.

We study the decay of the semigroup generated by the damped wave equation in an unbounded domain. We first prove under the natural geometric control condition the exponential decay of the semigroup. Then we prove under a weaker condition the logarithmic decay of the solutions (assuming that the initial data are smoother). As corollaries, we obtain several extensions of previous results of stabilization and control.

We solve Skorokhod's embedding problem for Brownian motion with linear drift (W_t + κ t)_t≥0 by means of techniques of stochastic control theory. The search for a stopping time T such that the law of W_T + κ T coincides with a prescribed law μ possessing the first moment is based on solutions of backward stochastic differential equations of quadratic type. This new approach generalizes an approach by Bass [3] of the classical version of Skorokhod's embedding problem using martingale representation techniques.

The empowerment formalism offers a goal-independent utility function fully derived from an agent's embodiment. It produces intrinsic motivations which can be used to generate self-organizing behaviors in agents. One obstacle to the application of empowerment in more demanding (esp. continuous) domains is that previous ways of calculating empowerment have been very time consuming and only provided a proof-of-concept. In this paper we present a new approach to efficiently approximate empowerment as a parallel, linear, Gaussian channel capacity problem. We use pendulum balancing to demonstrate this new method, and compare it to earlier approximation methods.

The ability to steer the state of a dynamical network towards a desired state within a time horizon is intrinsically dependent on the number of driven nodes considered, as well as the network’s topology. The trade-off between time-to-control and the minimum number of driven nodes is captured by the notion of the actuation spectrum (AS). We study the actuation spectra of a variety of artificial and real-world networked systems, modeled by fractional-order dynamics that are capable of capturing non-Markovian time properties with power-law dependencies. We find evidence that, in both types of networks, the actuation spectra are similar when the time-to-control is less or equal to about 1/5 of the size of the network. Nonetheless, for a time-to-control larger than the network size, the minimum number of driven nodes required to attain controllability in networks with fractional-order dynamics may still decrease in comparison with other networks with Markovian properties. These differences suggest that the minimum number of driven nodes can be used to determine the true dynamical nature of the network. Furthermore, such differences also suggest that new generative models are required to reproduce the actuation spectra of real fractional-order dynamical networks.

The Lagrange–Dirac interconnection theory has been developed for primitive subsystems coupled by a standard interaction Dirac structure, i.e. a structure of the form $D_{\mathrm{\text{int}}}={\mathrm{\Sigma }}_{\mathrm{\text{int}}}\oplus {\mathrm{\Sigma }}_{\mathrm{\text{int}}}^{\circ }$, where ${\mathrm{\Sigma }}_{\mathrm{\text{int}}}\subset T(T^{*}Q)$ is a regular distribution, ${\mathrm{\Sigma }}_{\mathrm{\text{int}}}^{\circ }\subset T^{*}(T^{*}Q)$ is its annihilator and $Q$ is the configuration manifold of the theory. In this work, we extend this theory to allow for parameter-dependent subsystems coupled by nonstandard interaction Dirac structures. This is done, first, by using the Dirac tensor product and, then, by using interaction forces. Both approaches are shown to be equivalent, and also equivalent to a variational principle. After that, we demonstrate the relevance of this generalization by investigating three applications. First, an electromechanical system is modeled; namely, a piston driven by an ideal DC motor through a scotch-yoke mechanism. Second, we relate the interconnection theory to the Euler–Poincaré–Suslov reduction. More specifically, we show that the reduced system may be regarded as an interconnected Lagrange–Dirac system with parameters. The nonholonomic Euler top is presented as a particular instance of this situation. Lastly, control interconnected systems are defined and a control for a planar rigid body with wheels is designed.

We compute the limit energy density of solutions of the linear wave equation in a thin three-dimensional domain, if the wavelength of the Cauchy data is bounded from below by the thickness of the domain. As an application, we obtain a geometric criterion for the uniform observability of solutions of a damped wave equation on such a domain.

In proportional-integral-derivative (PID) control, it is well known that the selection of a method to deal with noise is an important issue and various methods have been proposed. However, similar methods to determine the response to noise have not been studied in probability theory. In this paper, a new method called “weak form” is proposed and a probabilistic analysis of filtered derivatives is performed using this method. The method discussed in this paper is considered effective when it is not a feedback control.

Consciousness in higher animals, by virtue of its 100 ms time constant, is a necessarily greatly simplified and stripped-down version of more complex multiple tunable workspace cognition/ regulation dyads like wound healing, immune function, gene expression, institutional function and the like. These more complex dynamic entities emerged through evolutionary exaptation of the inevitable information crosstalk between coresident cognitive modules. In consequence of the debrided nature of consciousness, it should not be difficult to construct a fast, single workspace “conscious machine” that mimics the human tunable neuronal global workspace system. Tied to a “backbrain” AI that has learned hyperrapid stereotypic pattern responses to some particular set of likely challenges, the result is an elementary “emotional” conscious machine. A clever designer, however, may want to use available high-speed electronics to mimic the more capable multiple-workspace/ workforce systems inherently less susceptible to inattentional blindness and related failings of overfocus and thrashing. Contrary to current social constructions, however, the ultimate utility of such machines remains obscure. Here, we explore these matters in formal detail, restricting argument to the asymptotic limit theorems of information and control theories.

Real-world cognitive structures — embodied biological, machine or composite entities — are inherently unstable by virtue of the “topological information” imposed upon them by external circumstance, adversarial intent, and other persistent “selection pressures”. Consequently, under the Data Rate Theorem (DRT), they must be constantly controlled by embedding regulators. For example, blood pressure and the stream of consciousness require persistent delicate regulation in higher organisms. Here, using the Rate Distortion Theorem of information theory, we derive a form of the DRT of control theory that characterizes such instability for adiabatically stationary nonergodic systems and uncover novel forms of cognitive dynamics under stochastic challenge. These range from aperiodic stochastic amplification to Yerkes–Dodson signal transduction and outright system collapse. The analysis, deliberately closely adapted from recent purely biological studies, leads toward new statistical tools for data analysis, uncovering groupoid symmetry-breaking phase transition analogs to Fisher Zeros in physical systems that may be important for studies of machine intelligence under real-world, hence embodied, interaction. The challenges facing construction, operation, and stabilization of high-order “workspace” or “multiple-workspace” machine cognition, perhaps backed by rapid pattern-matching “emotional” AI, whether explicitly recognized as conscious or not, will require parallel construction of new analytic machinery. This work provides one example, solidly based on the asymptotic limit theorems of information and control theories.