Dwell Time Method Research Articles

Finite-time event-triggered filtering of the discrete-time switched linear systems with time delay

The finite-time event-triggered filtering of the discrete-time switched linear systems with time delay is addressed in the paper. The switched system and its filtering switched system are established as a filtering error system (FES) with augmented switching signal by the merging switching signal technique. The asynchronous switching phenomenon of switched system modes and filter modes occurs since a mode-dependent event-triggered transmission scheme (METS) which determines the system output and switching signal is addressed. Meanwhile, by the average dwell time (ADT) and multi-Lyapunov functional method, some sufficient conditions are given to make certain that the FES is finite-time bounded (FTB) and has a specified performance. Furthermore, the finite-time filter is designed by solving linear matrix inequalities. Ultimately, a numerical example is inspired to manifest the availability of the effects in the study.

A new computation method of minimum dwell time for the global asymptotic stability of switched linear differential systems

In this paper, switched linear systems are considered and dwell and average dwell time for their global asymptotic stability is examined. Dwell and average dwell time are determined based on the condition number for the global asymptotic stability of switched linear differential systems. Numerical examples which show the effect of the results obtained are given with the new dwell and average dwell times.

Fault Detection Filter Design and Optimization for Switched Systems with All Modes Unstable.

This problem of intelligent switched fault detection filter design is investigated in this article. Firstly, the mode-dependent average dwell time (MDADT) method is applied to generate the time-dependent switching signal for switched systems with all subsystems unstable. Afterwards, the switched fault detection filter is proposed for the generation of residual signal, which consists of dynamics-based filter and learning-based filter. The MDADT method and multiple Lyapunov function (MLF) method are employed to guarantee the stability and prescribed attenuation performance. The parameters of dynamics-based filter are given by solving a series of linear matrix inequalities. To improve the transient performance, the deep reinforcement learning is introduced to design learning-based filter in the framework of actor-critic. The output of learning-based filter can be viewed as uncertainties of dynamics-based filter. The deep deterministic policy gradient algorithm and nonfragile control are adopted to guarantee the stability of algorithm and compensate the external disturbance. Finally, simulation results are given to illustrate the effectiveness of the method in the paper.

Dynamic Event-Triggered Pinning Synchronization for Switched Impulsive Complex Networks With Asynchronous Switching

In this article, the pinning control problem is considered for the synchronization of switched impulsive complex networks (SICNs) with asynchronous switching. In order to reduce the communication burden, a pinning controller under the mode-dependent dynamic event-triggered (DET) scheme is designed to realize the synchronization. Unlike the conventional DET control strategies, this brief proposed one that simultaneously transmits the state and the switching information to the controller. Moreover, using the average dwell time method, a set of sufficient conditions for synchronization analysis is developed. Besides, the proposed control scheme can eliminate Zeno behavior effectively and even lessen the consumption of computing resources.

H∞$$ {H}_{\infty } $$ tracking control for uncertain switched stochastic systems with mixed time‐varying delays

AbstractThis article concerns the exponential tracking control problem of uncertain switched stochastic systems with mixed time‐varying delays including discrete delay and distributed delay. First, according to the multiple Lyapunov–Krasovskii functional described by the mixed time‐varying delays and the average dwell time method, a delay‐dependent sufficient conclusion is obtained, which makes the augmented system mean‐square exponential stable and satisfies the tracking performance. Then, the corresponding controllers are designed to ensure that the system has model reference tracking performance based on the above stability analysis. Finally, a numerical example and water quality preservation problems are employed to corroborate the usefulness of the method.

H ∞ Consensus Design and Online Scheduling for Multiagent Systems with Switching Topologies via Deep Reinforcement Learning

This paper is devoted to H ∞ consensus design and online scheduling for homogeneous multiagent systems (MASs) with switching topologies via deep reinforcement learning. The model of homogeneous MASs with switching topologies is established based on switched systems theory, in which the switching of topologies is viewed as the switching among subsystems. By employing linear transformation, the closed-loop systems of MASs are converted into reduced-order systems. The problem of H ∞ consensus design can be transformed to the issue of H ∞ control. It is supposed that the consensus protocol is composed of two parts: dynamics-based protocol and learning-based protocol, where dynamics-based protocol is provided to guarantee the convergence and weighted attenuation and learning-based protocol is proposed to improve the transient performance. Then, the multiple Lyapunov function (MLF) method and mode-dependent average dwell time (MDADT) method are combined to ensure the stability and weighted H ∞ disturbance attenuation index of reduced-order systems. The sufficient existing conditions of dynamics-based protocol are given through the feasible solutions of linear matrix inequalities (LMIs). Moreover, the online scheduling is formulated as a Markov decision process, and the deep deterministic policy gradient (DDPG) algorithm in the framework of actor-critic is proposed for the compensation of disturbance to explore optimal control policy. The online scheduling of parameters of MASs is viewed as bounded compensation of dynamics-based protocol, whose stability can be guaranteed by nonfragile control theory. Finally, simulation results are provided to illustrate the effectiveness and superiority of the proposed method.

Observer‐based finite‐time passive control of discrete‐time switched nonlinear systems with time‐delay

AbstractIn this paper, an observer‐based controller is designed to control a class of discrete‐time switched nonlinear systems with state delay and external disturbances. Based on the passivity concept, the average dwell time method, and auxiliary matrices, less‐conservative sufficient conditions are derived to make the closed‐loop system finite‐time bounded and passive in the presence of disturbances. In contrast to existing papers in this field, this paper deals with discrete‐time nonlinear switched systems and especially with an observer‐based controller. The developed conditions are presented in the form of linear matrix inequalities. Finally, computer simulations (numerical and practical examples) are provided to illustrate the performance of the proposed controller.

Intelligent L2-L∞ Consensus of Multiagent Systems under Switching Topologies via Fuzzy Deep Q Learning.

The problem of intelligent L2-L∞ consensus design for leader-followers multiagent systems (MASs) under switching topologies is investigated based on switched control theory and fuzzy deep Q learning. It is supposed that the communication topologies are time-varying, and the model of MASs under switching topologies is constructed based on switched systems. By employing linear transformation, the problem of consensus of MASs is converted into the issue of L2-L∞ control. The consensus protocol is composed of the dynamics-based protocol and learning-based protocol, where the robust control theory and deep Q learning are applied for the two parts to guarantee the prescribed performance and improve the transient performance. The multiple Lyapunov function (MLF) method and mode-dependent average dwell time (MDADT) method are combined to give the scheduling interval, which ensures stability and prescribed attenuation performance. The sufficient existing conditions of consensus protocol are given, and the solutions of the dynamics-based protocol are derived based on linear matrix inequalities (LMIs). Then, the online design of the learning-based protocol is formulated as a Markov decision process, where the fuzzy deep Q learning is utilized to compensate for the uncertainties and achieve optimal performance. The variation of the learning-based protocol is modeled as the external compensation on the dynamics-based protocol. Therefore, the convergence of the proposed protocol can be guaranteed by employing the nonfragile control theory. In the end, a numerical example is given to validate the effectiveness and superiority of the proposed method.

Resilient practical cooperative output regulation for MASs with unknown switching exosystem dynamics under DoS attacks

In this paper, the resilient practical cooperative output regulation problem (CORP) is addressed for heterogeneous linear multi-agent systems with unknown switching exosystem dynamics under denial-of-service (DoS) attacks. Different from most existing cooperative output regulation works, the exosystem dynamics considered in this paper are unknown to all agents and switching in different time intervals. A novel resilient practical cooperative output regulation control scheme is developed. This scheme consists of (i) a data-driven learning algorithm to learn the unknown switching exosystem matrices; (ii) an auxiliary observer to estimate the state of the exosystem; (iii) distributed resilient observers to estimate the state of the auxiliary system; and (iv) distributed controllers for individual agents. By using the dwell-time method, rigorous stability analysis shows that the resilient observation errors are globally ultimately bounded in the presence of DoS attacks and the resilient practical CORP is solved. Finally, a simulation example is given to illustrate the effectiveness of the proposed control scheme.

Adaptive event‐triggered output‐feedback control for switched nonlinear systems with time‐varying delays: A modified MDADT method

In this paper, the issue of adaptive event-triggered output-feedback control for a class of switched nonlinear systems with time-varying delays is investigated. By adopting the mode-dependent average dwell time (MDADT) method and the backstepping technique, an adaptive neural output-feedback control strategy is proposed for the switched system with event-triggered mechanism. In the process of controller design, an intelligent approximation technique and a switched filter are introduced to overcome the difficulties caused by the unknown nonlinear functions and the immeasurable states, respectively. Moreover, the appropriate Lyapunov–Krasovskii functionals are designed to compensate the effects of time delays. It is proved that the proposed control strategy guarantees that all the signals in the switched closed-loop systems are bounded under arbitrary switchings with MDADT. In the end, two simulation examples are provided to illustrate the feasibility of the developed control strategy.

Consensus of Lur’e Multi-Agent Systems With Directed Switching Topology

We study the consensus tracking problems of Lur’e multi-agent systems (MASs) with directed switching topology and a leader that is subject to unknown inputs. We firstly use the pure relative outputs to design a distributed unknown input observer (UIO) that can track the relative states exactly. Then we use this UIO to design a discontinuous controller which contains a consensus part and a discontinuous part, where the impacts of the leader’s unknown inputs can be completely removed by the discontinuous part. Furthermore, by using the average dwell time (ADT) method, we show that asymptotical consensus can be achieved if the ADT is larger than a positive threshold. Secondly, we design a continuous controller under which the consensus tracking error is uniformly ultimately bounded (UUB). Finally, we perform a simulation on the multiple Chua’s circuits to validate the theoretical result.

Stability analysis of nonlinear impulsive switched positive systems

Abstract In this paper, the global asymptotic stability (GAS) of continuous-time and discrete-time nonlinear impulsive switched positive systems (NISPS) are studied. For continuous-time and discrete-time NISPS, switching signals and impulse signals coexist. For both of these systems, using the multiple max-separable Lyapunov function method and average dwell-time (ADT) method, some sufficient conditions on GAS are given. Based on these, the GAS criteria are also given for continuous-time and discrete-time linear impulsive switched positive systems (LISPS). From our criteria, the stability of the systems can be judged directly from the characteristics of the system functions, switching signals and impulse signals of the systems. Finally, simulation examples verify the validity of the results.

Stability analysis for highly nonlinear switched stochastic systems with time-varying delays

In this paper, we examine the stability of highly nonlinear switched stochastic systems (SSSs) with time-varying delays, where the switching time instants are deterministic rather than stochastic. Herein, the boundedness of the global solution is first proven for highly nonlinear SSSs via the average dwell time (ADT) method and multiple Lyapunov function (MLF) approach. Then, the stability criteria for qth moment exponential stability and almost surely exponential stability are presented. The main difficulty lies in the presence of switching and time-varying delay terms, which prevents the validation of existing methods. New inequality techniques have been developed to counteract the effects of switching signals and time-varying delays. Finally, an example is provided to verify the effectiveness of the results.

Finite-time asynchronous control of discrete-time switched linear systems with event-triggered H∞ filtering

In this paper, the event-triggered H∞ filtering problem for discrete-time linear switched systems is investigated under asynchronous switching. Under the mode-dependent event-triggered transmission mechanism (METM), the switching signal and filtering signal are combined into an augmented switching signal by merging signal technology, and the switched system and filtering system are modeled as a filtering error system (FES). Because the switching signal of the filtering system is determined by METM, there will be an asynchronous switching phenomenon between the switched system and filtering system. The novel sufficient conditions are given to ensure that the FES is finite-time bounded (FTB) and has a specified H∞ performance by the average dwell time (ADT) and multi-Lyapunov functional method. And based on this, the design method of the H∞ filter is given. Ultimately, the numerical examples are inspired to manifest the availability of the effects in the study.

Robust asynchronous switching predictive control for multi-phase batch processes with time-varying tracking trajectory and delay

To solve the delay condition of the controller during adjacent phases and the change of the set value in multi-phase batch processes, a robust asynchronous switching predictive control scheme is proposed based on the mode-dependent average dwell time method. Firstly, the model of multi-phase batch processes including stable and unstable subsystems is established. Secondly, the LMI conditions to ensure that the system is asymptotically stable at each phase and exponentially stable at each batch are given. By solving these LMI conditions, not only the control law can be calculated, but also the shortest running time in the stable subsystems and the longest running time in the unstable subsystems can be obtained. Finally, according to these times, the controller is switched ahead of time to avoid the appearance of unstable subsystems. The comparison results of the injection moulding processes with the existing switching methods verifies the feasibility of the proposed method.

Adaptive tracking control of switched cyber-physical systems with cyberattacks

This study investigates the problem of adaptive tracking control for switched cyber-physical systems against cyberattacks. A tracking signal is generated using an exogenous system. An adaptive tracking controller is designed to compensate for the attacks and then stabilize the studied systems. A switching signal is constructed using the mode-dependent average dwell time (MDADT) method. By using the multiple Lyapunov function approach, which is associated with the adaptive estimated signal, the closed-loop error systems with cyberattacks are asymptotically stable under the designed adaptive tracking controller and MDADT switching signal, and the system states can asymptotically track the reference signal. Finally, two examples are provided to validate the theoretical results.

Non-weighted [formula omitted]/[formula omitted]-gain of asynchronously switched systems

This paper concerns that a non-weighted l2/L2-gain performance for asynchronously switched systems can be achieved in both discrete-time and continuous-time cases. Based on the constructed Lyapunov-like functions with average dwell time (ADT) method and inequality analysis technique, a non-weighted l2/L2-gain for asynchronously switched nonlinear systems can be guaranteed, which improves the existing results. Meanwhile, for asynchronously switched linear systems, the piecewise Lyapunov matrices are constructed and linear matrix inequalities (LMIs) conditions are derived to attain a non-weighted l2/L2-gain performance. Finally, some examples are provided to illustrate the theoretical results.

Stability of stochastic delay switched neural networks with all unstable subsystems: A multiple discretized Lyapunov-Krasovskii functionals method

This paper considers switching stochastic delay neural networks (SSDNNs) with all unstable subsystems. By using discretized Lyapunov-Krasovskii functions (DLKFs) combined with the dwell time method, exponential stability of SSDNNs with all unstable subsystems are analyzed, and several novel stability criteria in mean square are obtained. Comparing with the existing works, our results focus on all unstable subsystems rather than other combinations such as all stable or partially stable subsystems, which is of more research significance. Finally, the correctness of the conclusion is checked by the feasible solutions of two numerical examples.

Event-triggered L 2 − L ∞ filtering for asynchronous switched LPV systems with mode-dependent average dwell time

In this paper, event-triggered L 2 − L ∞ filtering problem for a class of switched linear parameter varying systems with both mode-dependent average dwell time and asynchronous switching is concerned. A new sampled delay-dependent and parameterised filtering error switched system is constructed on the basis of event-triggered communication scheme. Results on exponential stability with a prescribed L 2 − L ∞ performance are proposed by exploiting the parameter-dependent Lyapunov–Krasovskii functional and the mode-dependent average dwell time method, which is less rigid with requirement of minimal average dwell time of the switching signal. Furthermore, the gains of the parameter-dependent filter with mismatched system mode are solved in terms of linear matrix inequalities, meanwhile, the parallel results with the matched case are also obtained. Finally, a numerical example is provided to show the effectiveness and potential of the proposed design scheme.

Improved results on state estimation for switched continuous‐time linear systems

AbstractThis paper investigates the state estimation problem for switched linear systems involving additive disturbance and measurement noise, whose modes need not to be cooperative. Under the assumption that there exist nonsingular matrices that transform the observer error system matrices into Metzler ones, by using multiple Lyapunov functions and average dwell time method, hybrid state observers, which can produce a framer covering all possible state trajectories, are designed in two cases, that is, all the subsystems are stable and some of the subsystems may be unstable. The constructed interval observer for the considered systems are hybrid dynamical systems and the initialized states of the upper and lower observers at each switching instants are coupled, since the transformation matrices for different subsystems are different. Compared with the robust observer design for switched systems with arbitrary switching sequences in the literature, the difficulty consists in proposing new observer design conditions related to the state reset at the switching instants for switched systems under average dwell time scheme. Finally, two examples are given to show the efficiency of the proposed approach.