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The paper examines the perspectives of linear-quadratic (LQ) optimal control in steering the process of goods distribution in logistic systems with multiple transportation options. In the considered class, the distribution centre governs the stock replenishment process of subordinate depots, from which un uncertain market demand is served. The centre is linked with the depots via shared supply channels with different characteristics regarding delay, reliability, and capacity, e.g. train vs truck delivery. The design objective is a rule of dynamical channel allocation – how many goods to send in a period using a given mode – so that balanced, cost-efficient system performance and high customer service rate are achieved. The received goods are inspected for quality defects and rejected when faulty. Thus, one needs to cope with two major sources of uncertainty: unpredictable demand variations and channel imperfections. A multi-variable LQ optimal controller is designed and presented in closed form for detailed analytical and numerical treatment. It is formally shown that despite perturbations, the controller always establishes a non-negative and upper-bounded replenishment signal, and the stock level does not cross the reference value. Conditions for warehouse space selection and obtaining full demand satisfaction at the depots are specified and formally proved. [ABSTRACT FROM AUTHOR]

This work addresses the global exponential stability of nonlinear delayed discrete-time systems with Markovian switching. By a novel approach, some explicit criteria for the exponential stability in mean square of such systems are derived. An application to discrete-time neural networks is presented. [ABSTRACT FROM AUTHOR]

This paper is concerned with the stability analysis of discrete‐time systems with a time‐varying delay. The conservatism and computation burden are two important factors to evaluate a stability condition. By taking the relationship of two reciprocally convex parts into consideration, a new combined matrix‐separation‐based inequality is proposed that involves only a few free matrices. Moreover, an improved matrix‐injection‐based transformation lemma with the parameter varying within a closed interval is proposed by introducing only one free matrix. By constructing an appropriate Lyapunov–Krasovskii functional and applying the improved methods, a relaxed stability condition is consequently obtained with a small number of decision variables. Two numerical examples are given to show the merits of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper presents a joint synthesis algorithm of trajectory and controlled invariant funnel (CIF) for locally Lipschitz nonlinear systems subject to bounded disturbances. The CIF synthesis refers to a procedure of computing controlled invariance sets and corresponding feedback gains. In contrast to existing CIF synthesis methods that compute the CIF with a predefined nominal trajectory, our work aims to optimize the nominal trajectory and the CIF jointly to satisfy feasibility conditions without the relaxation of constraints and obtain a more cost‐optimal nominal trajectory. The proposed work has a recursive scheme that mainly optimize trajectory update and funnel update. The trajectory update step optimizes the nominal trajectory while ensuring the feasibility of the CIF. Then, the funnel update step computes the funnel around the nominal trajectory so that the CIF guarantees an invariance property. As a result, with the optimized trajectory and CIF, any resulting trajectory propagated from an initial set by the control law with the computed feedback gain remains within the feasible region around the nominal trajectory under the presence of bounded disturbances. We validate the proposed method via two applications from robotics. [ABSTRACT FROM AUTHOR]

This article pursues the robust consensus for linear discrete‐time multi‐agent systems with unknown dynamics and random uncertain channels. Stochastic multiplicative uncertainties depending on relative states of agents inevitably appear in the signal transmission channels. To handle these uncertainties, the distributed robust controllers are designed. Before designing this robust controller, the optimal control problem of a single‐agent system is considered first. Based on the technology of adaptive dynamic programming, a model‐free off‐policy algorithm is proposed to solve the optimal controller for every agent with fully unknown system dynamics. According to the theory of mean square stability, it is revealed that the distributed robust controller can be obtained by using the optimal controller of the single‐agent system and other related parameters without relying on the dynamic information of the systems. Besides, the relationship between uncertainty and the robust controller is described by a sufficient condition. Finally, to demonstrate the effectiveness of the theoretical analysis, a numerical example is presented. [ABSTRACT FROM AUTHOR]

With rising demands on system performance and reliability in engineering practice, researchers are increasingly interested in disturbance rejection control, of which state and disturbance observation is the essential element. The extended state observer (ESO, or extended high‐gain observer) is extensively utilized to compensate disturbance, nevertheless, the neglect of lumped disturbance's first derivative and peak phenomenon in classical ESO design impose obstacles to further promotion. In this article, nested ESO (NestedESO) is proposed to estimate states and disturbance simultaneously for general uncertain nonlinear systems under time‐varying disturbance. In NestedESO framework, low‐gain generalized ESO is implemented to obtain a rough estimation of lumped disturbance in the first stage. Then, a novel proportion‐filter‐derivative disturbance estimation refinement mechanism is introduced to provide accurate disturbance estimation. With refined disturbance estimation, modified Luenburger observer is put forward to reconstruct state. Besides, extension to sampled‐data systems is investigated to adapt the networked signal transmission scenario. Numerical examples are given to illustrate the validity and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In the realm of control engineering applications, compensating for unknown dynamics and nonlinearities is of paramount importance for shaping closed-loop performance. This paper introduces a novel solution to this challenge: the adaptive controller based on Quantum-Inspired Fuzzy Rules Emulated Network (QFREN). Leveraging its intrinsic learning capacity, QFREN assimilates human knowledge through a series of IF-THEN rules based on quantum computation principles. By defining quantum states for membership functions, the concept of coherent superposition of tracking errors is employed to effectively mitigate the effects of disturbances and nonlinearities. Learning laws are derived to finely calibrate all network and quantum computation parameters, accompanied by a thorough analysis of closed-loop performance to ensure robustness. Experimental validation and comparative assessments substantiate the efficacy of the proposed scheme, showcasing a reduction in tracking error of at least 20 % compared to recent comparative controllers based on data-driven and quantum-neural network schemes. [ABSTRACT FROM AUTHOR]

The distributed leader-follower control of multi-agent systems is discussed. Each agent is expressed in a discrete-time and non-linear dynamic model with an unknown parameter and can be affected by its neighbors' history information. For each agent, to identify the parameter, one switching set of the parameter estimates is constructed and the optimal parameter estimate is chosen based on the index switching function. Using the given desired reference signal, the leader agent's control law is designed, and relying on the neighbors' history information, each follower agent's local control law is designed. With the designed distributed tracking adaptive control laws, the whole system tracks the given desired reference signal, and in the face of strong couplings the closed-loop system ultimately reaches an agreement. Finally, by comparing simulations of the control strategy with a normal projection algorithm, the results indicate that the adaptive control method with a switching set of the parameter estimates is effective in improving the control performance. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of parameter identification for discrete-time stochastic systems with unknown exogenous inputs. These systems form an important class of dynamic stochastic system models used to describe objects and processes under a high level of a priori uncertainty, when it is not possible to make any assumptions about the evolution of the unknown input signal or its statistical properties. The main purpose of this paper is to construct a new SVD-based modification of the existing Gillijns and De Moor filtering algorithm for linear discrete-time stochastic systems with unknown exogenous inputs. Using the theoretical results obtained, we demonstrate how this modified algorithm can be applied to solve the problem of parameter identification. The results of our numerical experiments conducted in MATLAB confirm the effectiveness of the SVD-based parameter identification method that was developed, under conditions of unknown exogenous inputs, compared to maximum likelihood parameter identification when exogenous inputs are known. [ABSTRACT FROM AUTHOR]

The problem of constructing reachable and null-controllable sets for stationary linear discrete-time systems with a summary constraint on the scalar control is considered. For the case of quadratic constraints and a diagonalizable matrix of the system, these sets are built explicitly in the form of ellipsoids. In the general case, the limit reachable and null-controllable sets are represented as fixed points of a contraction mapping in the metric space of compact sets. On the basis of the method of simple iteration, a convergent procedure for constructing their external estimates with an indication of the a priori approximation error is proposed. Examples are given. [ABSTRACT FROM AUTHOR]

This paper investigates decentralised adaptive control of discrete‐time systems consisting of linear time‐invariant systems and a class of nonlinear systems. The parameters of the subsystems and the interconnection strengths between the subsystems are assumed unknown. Multiple adaptive prediction models with switching are used in this paper to address the relatively poor transient performance that typically results from a single prediction model. However, the application of this methodology requires indirect model reference discrete‐time adaptive control, and there appears to be very little focus in the literature on this. The principal contribution of this paper is to fill this void by arriving at proof of global stability of such decentralised adaptive systems using the theory of Lyapunov and properties of square‐summable sequences. The chosen representation of the system enables the same results to be directly applicable to both linear time‐invariant and linear‐in‐the‐parameters nonlinear subsystems. We consider two parametric update algorithms, one of which has a normalisation factor. Simulation studies included in this paper demonstrate the improvement in transient performance. [ABSTRACT FROM AUTHOR]

This paper concentrates on the finite-time  H ∞  control problem for a type of stochastic discrete-time Markovian jump systems, characterized by time-delay and partly unknown transition probabilities. Initially, a stochastic finite-time (SFT)  H ∞  state feedback controller and an SFT  H ∞  observer-based state feedback controller are constructed to realize the closed-loop control of systems. Then, based on the Lyapunov–Krasovskii functional (LKF) method, some sufficient conditions are established to guarantee that closed-loop systems (CLSs) satisfy SFT boundedness and SFT  H ∞  boundedness. Furthermore, the controller gains are obtained with the use of the linear matrix inequality (LMI) approach. In the end, numerical examples reveal the reasonableness and effectiveness of the proposed designing schemes. [ABSTRACT FROM AUTHOR]

This paper deals with the problems of robust exponential stability for a class of uncertain discrete-time switched systems with time-varying delay and linear fractional perturbations parametric uncertainties, under arbitrary switching signal on the one hand and by using the Average Dwell Time (ADT) approach on the other hand. Firstly, new sufficient conditions guaranteeing the exponential stability of the nominal considered system are proposed and proved, by constructing an augmented Lyapunov–Krasovskii functional, by using the discrete Wirtinger-based inequality combined with an improved form of Reciprocally Convex Lemma (RCL) and by considering the two types of switching signal mentioned above. Then, and based on the obtained results, new criteria are established to ensure the robust exponential stability for uncertain discrete-time switched systems with interval time-varying delay. The established conditions are dependent on the lower and the upper delay bounds and are expressed in terms of Linear Matrix Inequalities (LMIs). Furthermore, some slack variables are introduced by using the Finsler lemma in order to give more relaxation for the studied system. Consequently, the proposed approach is proved to have some less conservative results over than some recent works of the literature. Finally, numerical examples are provided to demonstrate the merit and the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper deals with the finite and infinite horizon filtering problems for discrete-time Markov jump linear systems. We assume that only an output and the jump parameters are available to the filter and the goal is to obtain a "prediction–correction" formula which is optimal among the Markovian filters. As in the case with no jumps, we show that an optimal filter can be obtained from a set of coupled Riccati difference and algebraic equations associated with the filtering problem. When there is only one mode of operation, our results coincide with the traditional Kalman filter for discrete-time linear systems. [ABSTRACT FROM AUTHOR]

This paper proposes a discrete-time model for dynamic trading, interconnecting cash and asset stocks. The trading action or control is based on the evolution of the asset prices, and any suitable asset price predictor can be used. Based on the model introduced, a one step ahead optimal control strategy, based on linear programming, is proposed. This leads to a trading algorithm which specfies a rule to buy or sell assets in a given portfolio. The addition of trade trigger logic to the basic scheme is also proposed, in order to allow return and risk to be traded off in the dynamic one step ahead trading scheme. The proposed one step ahead optimal policy is independent of the predictor of prices and their variances, chosen in this paper as the moving average, but replaceable by any desired estimator. Numerical examples are given to show that the proposed strategy performs reasonably well, with and without risk reduction, over datasets relating to different portfolios (banks, computers, ETFs and stocks). [ABSTRACT FROM AUTHOR]

The fault-tolerant tracking control problem is studied for the discrete-time systems with actuator faults. To lessen adverse impacts of actuator fault, a PPD information-driven fault estimation algorithm is established to adaptively estimate actuator fault information online, which avoids the additional construction and training process of neural network. With the aid of the adaptive fault compensation, a model-free adaptive fault-tolerant tracking control algorithm is constructed to ensure that the expected output reference trajectory can be tracked by system output. Moreover, only input and output data are employed throughout the design process, system dynamics are not demanded. Ultimately, the availability of developed strategy is proved through a simulation. [ABSTRACT FROM AUTHOR]

In this paper, a novel methodology is introduced for the inverse optimal control of non-affine, nonlinear and discrete-time systems. Although inverse optimal control of affine systems is studied in detail in technical literature, there is no adequate research about its implementation on non-affine systems. here are two main contributions of this work. Firstly using the input–output data of the system to be controlled its NARMA-L2 model is obtained using a multi-layer feedforward neural network, this step provides a conversion from a non-affine to affine system model. After the affine system model is obtained, the inverse optimal control law is applied. The second contribution of this paper is the computation of the inverse optimal control signal. The selection of the P matrix in the control law is crucial since its value directly affects the control performance. Here a novel method is proposed where an adaptive and optimal P matrix is computed online using a recurrent neural network to minimize a predefined cost function. The performance of the proposed control method is evaluated by simulations performed on benchmark problems. The robustness of the method is also tested by additional simulations where noise and disturbance is imposed on the system. The obtained results justify the applicability of the proposed approach. [ABSTRACT FROM AUTHOR]

The problem of consensus control of linear discrete-time multi-agent systems (MASs) with switching topology is considered in the presence of a leader. The goal of consensus control is to bring the states of all agents to the leader state while providing stability for local agents, as well as the MAS as a whole. In contrast to the traditional approach, which uses the concept of an extended dynamic multi-agent system model and communication topology graph Laplacian, this paper proposes a decomposition approach, which provides a separate design of local controllers. The control law is chosen in the form of distributed feedback with discrete PID controllers. The problem of local controllers’ design is reduced to a set of semidefinite programming problems using the method of invariant ellipsoids. Sufficient conditions for agents’ stabilization and global consensus condition fulfillment are obtained using the linear matrix inequality technique. The availability of information about a finite set of possible configurations between agents allows us to design local controllers offline at the design stage. A numerical example demonstrates the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper investigates the output-feedback control for discrete-time switched linear systems. By extending the methodology of switched Lyapunov functions (SLF), a non-monotonic SLF approach is proposed to analyse the stability of the resulting closed-loop system under arbitrary switching. This approach relaxes the requirement of monotonicity to conventional SLF approach, and hence it will lead to less conservative results. First, the stability of discrete-time switched systems is analysed, and then an output-feedback controller design method is proposed based on the obtained stability results. The controller design problem is formulated in term of LMIs, and relaxed variables are introduced in the synthesis conditions to improve the design freedom. Finally, three examples are used to verify the effectiveness and application potential of the proposed methods. [ABSTRACT FROM AUTHOR]

A contraction metric for a discrete-time dynamical system given by an autonomous iteration is a Riemannian metric such that the distance between adjacent solutions contracts over time. A contraction metric can be used to determine the basin of attraction of a fixed point and it is robust to small perturbations of the system, including those varying the position of the fixed point.In this paper, we prove a converse theorem, showing the existence of a contraction metric, which is the solution of a matrix-valued equation. We then develop a construction method based on meshless collocation to approximate the solution of this equation. Error estimates imply that a sufficiently close approximation is itself a contraction metric. The method is applied to several examples. [ABSTRACT FROM AUTHOR]

Summary: This paper proposes a systematic framework for stability and guaranteed cost control of linear impulsive systems subject to random time‐ and event‐triggering impulses. Moment stability criteria and design methods of time‐ and event‐triggered controllers with guaranteed quadratic performance for the impulsive system are established. It shows that the proposed event‐triggered controller in the sense that it guarantees at least the same quadratic performance function bound as the designed time‐triggered guaranteed cost controller, however, with a larger, or at most equal, average inter‐transmission time. Based on the proposed framework of random‐impulses systems, a stochastic dynamic event‐triggered control strategy is proposed to solve sampled‐data control systems in the presents of sporadic measurements or stochastic sampling. Numerical simulations illustrate the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

Given an unstable (or stable) impulsive Markovian switching system (IMSS), can it be stabilized (or destabilized) by noise? This problem has not been studied. In view of this question, this article will establish the noise stabilization and destabilization strategies of IMSS, and also study the impulsive control realized by adjusting the impulse intensity. It is worth noting that the impulse jump is the random impulse whose jump value depends on the mode, and the noise stabilization and destabilization are realized by periodic stochastic control based on Lévy noise. In order to establish these new results, we use the time‐inhomogeneous property of coefficients of the controlled system and the ergodicity of discrete‐time Markov chains based on impulse trigger time. In addition, the periodic stochastic control on diffusion and jump terms can be applied to design intermittent stochastic control. [ABSTRACT FROM AUTHOR]

A neural network (NN) optimal control for discrete-time nonlinear dynamic systems with known internal dynamics is designed. The control is described by an algebraic equation with a variable structure. This algebraic equation is derived analytically. A functional block diagram of the controlled system is given and analyzed. Software and hardware implementation aspects of the controller are discussed. The controller does not need any training and has moderate complexity. The discrete-time state variable trajectories of the controlled system are shown to be globally asymptotically stable and convergent to unique steady states. It is proved that these trajectories converge to steady-state neighborhood in a finite number of steps. Sliding mode analysis of controller operation is fulfilled. A correctness of controller operation in the case of disturbances of its nonlinearities is analyzed. Using the controller for a special case of optimal tracking control is discussed. Results of presented computer simulations of optimal control of discrete-time two-dimensional and three-dimensional affine nonlinear systems and optimal tracking control of permanent-magnet motor of linear type applied for accurate positioning and nonlinear cooling continuous stirred tank reactor confirm theoretical statements of the paper and illustrate a performance of the controller. [ABSTRACT FROM AUTHOR]

In this paper, exponential stability of continuous-time and discrete-time switched $ k\times k $ k × k block triangular systems under arbitrary switching is studied. Firstly, under the assumption that all subsystem matrices are Hurwitz and a family of those corresponding block diagonal matrices is commutative, we prove that a continuous-time switched linear system is exponentially stable under arbitrary switching. Next, under the assumption that all subsystem matrices are Hurwitz and all those block diagonal matrices are normal, it is shown that the same switched system is exponentially stable under arbitrary switching. Further, under similar conditions we prove that a discrete-time switched linear system is exponentially stable under arbitrary switching. After that, illustrative numerical examples of the obtained results are also given. Finally, we prove that $ 3\times 3 $ 3 × 3 normal matrices have nine parameter representations which are useful for numerical examples (in the Appendix). [ABSTRACT FROM AUTHOR]

This paper proposes a novel learning‐based model predictive control (LMPC) scheme for discrete‐time nonlinear systems. It overcomes the challenge of manually designing the terminal conditions for traditional MPC and enhances the control performance. The scheme employs the value iteration (VI) in reinforcement learning (RL), and autonomously designs the terminal cost by iteratively performing value function learning and policy update under known dynamics and constraints. In contrast to the existing schemes that combine RL with MPC, the proposed scheme explicitly considers the approximation errors in each iteration. Further, a rigorous theoretical analysis is provided, including the convergence of VI, the stability and performance of the closed‐loop system. In addition, the influences of the prediction horizon and the initial terminal cost on performance are also investigated. Simulation results of a linear system verify the theoretical properties of the LMPC and show that it achieves (near‐)optimal performance. Moreover, its unique superiority over traditional MPC is fully demonstrated in a nonholonomic vehicle regulation example. [ABSTRACT FROM AUTHOR]

Summary: This paper investigates the robustness of exponential stability of a class of positive switched systems described by linear functional differential equations (FDE) under arbitrary switching or average dwell time switching. We will measure the stability robustness of such a system (which is considered as a nominal system) subject to parameter affine perturbations of its constituent subsystems matrices, by introducing the notion of structured stability radius. Some formulas for computing this radius, as well as estimating its lower bounds and upper bounds, are established. In the case of switched linear systems with multiple discrete time‐delays or/and distributed time‐delays, the obtained results yield tractably computable formulas or bounds for the stability radius. The extension of the obtained results to non‐positive systems and the class of multi‐perturbations has been presented. Examples are given to illustrate the proposed method. [ABSTRACT FROM AUTHOR]

In this article, a distributed diffusion Kalman filtering algorithm with event‐triggered communication (DDKF‐E) is studied for discrete‐time nonlinear systems. According to the event‐triggered communication protocol, the data between sensors and estimators are transmitted only when the predefined conditions are satisfied. Considering the characteristic of event‐triggered method and truncated error by linearization, an upper bound of the estimation error covariance matrix is obtained by using the variance‐constrained method. The Kalman gain is designed to minimize the upper bound and then two Riccati equations are obtained. Furthermore, the stochastic stability theory is used to prove the stability of DDKF‐E, and it is derived that the estimation error of DDKF‐E is exponentially bounded in mean square. Finally, numerical simulations validate the effectiveness of the DDKF‐E algorithm. [ABSTRACT FROM AUTHOR]

This paper studies the exponential stabilization problem for a class of discretetime linear switched systems arising from establishing the output-based distributed observer and the output-based adaptive distributed observer for discrete-time linear leader systems over jointly connected switching networks. The existing results on distributed observers and adaptive distributed observers are state-based in the sense that they need to make use of the full state of the leader system, which is quite restrictive since, in many applications, only the output of the leader system is available. As an application, the output-based distributed observer is used to solve a leader-following consensus problem for discrete-time linear multiagent systems by distributed output feedback control. [ABSTRACT FROM AUTHOR]

Aiming at resolving the parameter uncertainty of the servo system under multi‐working conditions, a flatness‐based switched linear system model is proposed. Firstly, a fifth‐order linear switched discrete‐time system with uncertain parameters is established. The flatness properties of switched system is described and a de Bruijn's graph‐based framework is introduced for graphical description of the switched system. In addition, non‐linear bode diagrams are obtained via sweeping signals with multiple amplitudes. The discrete equations of the electromechanical servo system are established by the bode plots. The unknown parameters of the subsystems in switched model are identified by the simulated annealing algorithm, and compared with the least squares method to verify the accuracy of the identified parameters. Finally, the simulation model and experimental platform are constructed to verify the effectiveness of the proposed method. The switched model is compared with the classical transfer function model and single subsystems. The results indicate that the resolution of parameter uncertainty in servo systems is effective. The accuracy of the established switched model is about 99.5%. The accuracy of the switched linear system model of the electromechanical servo system is verified and the proposed modelling method is validated. [ABSTRACT FROM AUTHOR]

This article presents a novel approach to maintaining connectivity within a multi-agent system (MAS) using directional visual sensors. The approach leverages a mathematical model of the sensors and employs an optimization method to determine the position and orientation constraints for each sensor. Experimental results validate the effectiveness of the approach for a range of tasks within MAS. The text also discusses a three-step procedure for computing the desired position and orientation of a group of agents. It introduces an optimization problem for a given task and presents a gradient-descent approach to solve it. The text discusses the control objective of designing appropriate control actions for each agent to track a sequence of targets while considering the limitations of visual sensors. The main results involve establishing sufficient conditions for fulfilling the control objective and designing upper bounds for linear and angular velocity. The text also discusses a three-step control law for maintaining connectivity between agents in a network. The control law is designed to be fully distributed and ensures connectivity within the network. The given text discusses a distributed algorithm for maintaining connectivity in a multi-agent system with limited and directional sensing capabilities. The algorithm ensures that each sensor's control variables remain within their upper bounds while preserving connectivity. The effectiveness of the algorithm is validated through simulation and experimental results. The text provides brief biographical information about two individuals, one named D. degree and the other named Denny Oetomo, who have expertise in robotics and system dynamics. [Extracted from the article]

This document provides brief biographical information about three individuals involved in the field of mathematics and systems science. The first individual is a professor at the ISS Academy of Mathematics and Systems Science, CAS, with research interests in system modeling, adaptive control, stochastic systems, and multi-agent systems. The second individual is a professor at Beijing Institute of Technology, specializing in adaptive control, quantized control, multi-agent systems control, and their applications to aircraft control systems. The third individual is a Ph.D. student at the Academy of Mathematics and Systems Science, with research interests in quantized control, adaptive control, and sparse identification. [Extracted from the article]

In the work, we prove the presence of chaotic dynamics, for suitable values of the model parameters, for the discrete-time system, composed of two coupled logistic maps, as formulated in Yousefi et al. [Discrete Dyn. Nat. Soc. 5, 161–177 (2000)], which describes two interdependent economies, characterized by two competitive markets each, with a demand link between them. In particular, we rely on the SAP (Stretching Along the Paths) method, based on a stretching relation for maps defined on sets homeomorphic to the unit square and expanding the paths along one direction. Such technique is topological in nature and allows to establish the existence of a semiconjugacy between the considered dynamical system and the Bernoulli shift, so that the main features related to the chaos of the latter (e.g., the positivity of the topological entropy) are transmitted to the former. In more detail, we apply the SAP method both to the first and to the second iterate of the map associated with our system, and we show how dealing with the second iterate, although being more demanding in terms of computations, allows for a larger freedom in the sign and in the variation range of the linking parameters for which chaos emerges. Moreover, the latter choice guarantees a good agreement with the numerical simulations, which highlight the presence of a chaotic attractor under the conditions derived for the applicability of the SAP technique to the second iterate of the map. [ABSTRACT FROM AUTHOR]

This paper concerns an improved model-free adaptive fractional-order control with a high-order pseudo-partial derivative for uncertain discrete-time nonlinear systems. Firstly, a new equivalent model is obtained by employing the Grünwald–Letnikov (G-L) fractional-order difference of the input in a compact-form dynamic linearization. Then, the pseudo-partial derivative (PPD) is derived using a high-order estimation algorithm, which provides more PPD information than the previous time. A discrete-time model-free adaptive fractional-order controller is proposed, which utilizes more past input–output data information. The ultimate uniform boundedness of the tracking errors are demonstrated through formal analysis. Finally, the simulation results demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper studies the average consensus tracking problem of first-order multi-agent systems under directed topologies. A control protocol is constructed based on the neighbors' agent sampled information. With the help of the matrix theory and frequency domain analysis, the necessary and sufficient condition can be induced for the average consensus tracking of multi-agent systems, although the weight-balanced condition is not satisfied. In addition, a numerical simulation example is given to illustrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]