Average Dwell Time Method Research Articles

Adaptive threshold scheme for fault detection for positive switched systems with parametric uncertainty

This paper addresses the challenge of designing a fault detection observer for actuators and sensors in a particular class of positive switched systems, using the average dwell time method. The proposed approach involves the concurrent generation of residuals and a dynamic threshold, enhancing the precision and efficiency of fault detection. Additionally, our work introduces an innovative method for fault detection with parametric uncertainties, outlining sufficient conditions for designing the observer using Linear Programs (LP). The effectiveness of the proposed approach is validated through a numerical simulation.

Dynamic output feedback model predictive control for polytopic uncertain systems under decode and forward cooperative relay protocol

This paper addresses the robust model predictive control (RMPC) problem for a class of polytopic uncertain systems under the decode and forward cooperative relay protocol (DFCP). In order to combat signal fading from sensors to controllers and improve communication reliability, spatial diversity is achieved through cooperative terminal relay signals. At each transmission instant, the terminal only selects a better signal for transmission and a switched system is constructed. The aim of this paper is to design a set of desired dynamic output feedback controllers in the framework of RMPC such that the switched system with the underlying DFCP is exponentially stable. By taking the influence of the randomness of DFCP derived from a three nodes model composed of DF relay, a new objective function based on the mathematical expectation of the traditional quadratic function of MPC is established. Then, the orthogonal complement technique is applied to handle the inherent couplings of variables to formulate a solvable optimisation problem. Moreover, the sufficient conditions are provided to guarantee the recursive feasibility of the MPC strategy and the stability of the established closed-loop system in terms of the average dwell time (ADT) method. Finally, three experiments are given to illustrate the effectiveness of the proposed method.

Simultaneous fault-tolerant consensus control and disturbance suppression for multi-agent systems with polynomial form fault under switching topology

For continuous-time linear leader-follower multi-agent systems with polynomial faults, the problem of fault-tolerant state consensus under switching topologies is studied. firstly, the average dwell time method is introduced, and observers are designed for different topologies to observe faults and disturbances. Secondly, according to the observed estimated value, the corresponding fault-tolerant control consensus protocol is proposed considering the switching situation of the communication topology. Finally, both theoretical analysis and simulation examples verify that the proposed design scheme can compensate faults and disturbance rejection.

Model predictive control for space robot manipulator modeled by switched systems: A data‐driven approach

AbstractThis article investigates the data‐driven based model predictive control (MPC) problem for a class of space robot manipulator (SRM). First, the SRM system is modeled as a class of discrete‐time switched system to reflect more system characteristics. Second, only the input‐state data are used for end‐to‐end controller design, and the system identification process is avoided. In order to meet the real‐time requirements of the manipulator arm angles, a kind of constrained predictive control method is designed to prevent the overheating or damage of SRM motor, optimizing the cost function for each decision cycle under the safe control input constraints. Then, based on the average dwell time method, the asymptotic stability is assured for the presented SRM system. The design conditions for data‐driven based MPC are provided in the form of linear matrix inequalities. Finally, the effectiveness and advantage for the developed data‐driven based MPC strategy are validated via a case study of SRM system.

Event-triggered and quantised feedback stabilisation of switched networked control systems

In order to conserve network resources, this paper investigates the event-triggered control and quantised feedback stabilisation of switched networked control systems by introducing the vector quantizer technique. The state information undergoes quantisation and is transmitted to the controller after being sampled by the event-triggering technology. The designed event-triggered mechanism relies on quantised state values, and the generation of each quantised value also depends on the event-triggered condition. Addressing the asynchronous issue between the controller and the subsystem, we provide a sufficient condition for ensuring exponential stability of the closed-loop system and outline the controller gain design method by employing the multiple Lyapunov function and average dwell time methods. Besides, we demonstrate the explicit exclusion of the Zeno phenomenon in the event-triggered mechanism. Finally, the viability of our approach is demonstrated through simulation examples.

Event‐triggered anti‐disturbance control for switched singular systems based on the uncertainty and disturbance estimator

AbstractThis article studies the event‐triggered anti‐disturbance control problem for switched singular systems (SSSs) based on the uncertainty and disturbance estimator (UDE). First, a composite controller consisting of feedback control and anti‐disturbance control based on UDE is proposed. By constructing the multiple Lyapunov functions and using the average dwell time (ADT) method, sufficient conditions are given to ensure that the closed‐loop system is regular, impulse‐free and globally uniformly asymptotically stable (GUAS). Further, in order to save resources, the event‐triggered control method is introduced into the feedback control, and a novel hybrid event‐triggered mechanism (ETM) is proposed, which guarantees that asynchronous switching and Zeno behavior are excluded. And the solvable conditions in terms of linear matrix inequalities (LMIs) are given. Finally, the validity of the proposed results is verified by the simulations.

Dynamic event‐triggered H∞ control for switched T‐S fuzzy systems under multiple cyber attacks

SummaryThis article studies the dynamic event‐triggered control problem for switched Takagi‐Sugeno (T‐S) fuzzy systems against multiple cyber attacks. A new multiple cyber attack model is established by considering random false data injection attacks and aperiodic denial‐of‐service attacks. Then, to further efficiently utilize network communication resources, a dynamic event‐triggered mechanism (ETM), which includes a nonnegative dynamic variable, is constructed. Furthermore, the time‐delay switched T‐S fuzzy system considering dynamic ETM and multiple cyber attacks is derived by utilizing model transformation methods. Moreover, sufficient conditions for globally asymptotically stability and performance are derived by utilizing multiple Lyapunov functions and average dwell time method. Finally, an example is provided to validate the effectiveness of dynamic ETM.

Dynamic event‐triggered asynchronous output feedback control for discrete‐time switched systems with deception attacks

AbstractThis article addresses the problem of dynamic event‐triggered asynchronous output feedback controller design for discrete‐time switched systems under deception attacks. To conserve communication resources and restrict asynchronous time, a dynamic event‐triggered mechanism is established which permits the system to switch many times in the trigger interval. Then, stability criteria for the underlying system despite the impact of deception attacks are obtained via the Lyapunov function and average dwell time method. Meanwhile, a co‐design scheme for dynamic output feedback gains and dynamic event‐triggered parameters are provided. Finally, two simulations are used to demonstrate the effectiveness of the approach.

Robust stabilization of uncertain switched nonlinear systems via saturated impulsive control

AbstractThis article investigates the stabilization problem of uncertain switched nonlinear systems. Uncertainty and saturated impulses are first considered together in switched nonlinear systems. It appears that the considered systems are robustly locally exponentially stable under the fast average dwell time method and the designed saturated impulsive controller even though subsystems are unstable. At the same time, our conclusions cover some previous results. A step‐by‐step strategy for optimizing multiple objectives is designed to estimate the basin of attraction of the systems as large as possible. At last, the efficacy of our conclusions is illustrated by two given examples.

Distributed Nash equilibrium seeking in noncooperative game with partial decision information of neighbors.

In the real world, individuals may conceal some of their real decision information to their neighbors due to competition. It is a challenge to explore the distributed Nash equilibrium when individuals play the noncooperative game with partial decision information in complex networks. In this paper, we investigate the distributed Nash equilibrium seeking problem with partial decision information of neighbors. Specifically, we construct a two-layer network model, where players in the first layer engage in game interactions and players in the second layer exchange estimations of real actions with each other. We also consider the case where the actions of some players remain unchanged due to the cost of updating or personal reluctance. By means of the Lyapunov function method and LaSalle's invariance principle, we obtain the sufficient conditions in which the consensus of individual actions and estimations can be achieved and the population actions can converge to the Nash equilibrium point. Furthermore, we investigate the case with switched topologies and derive the sufficient conditions for the convergence of individual actions to Nash equilibrium by the average dwell time method. Finally, we give numerical examples for cases of fixed and switched topologies to verify our theoretical results.

Input-to-state stability of discrete-time impulsive switched delayed systems with delay-dependent impulse under two asynchronous cases

This paper studies a class of discrete-time impulsive switched delayed systems with delay-dependent impulses, aiming to solving the input-to-state stability (ISS) problem in the case of asynchronous switching signal between subsystem and controller and asynchrony of switching signals and impulsive signals. Among them, the delay effect is handled by a new Lyapunov-Krasovskii function divided into a delay-dependent part and a delay-independent part. In contrast to admissible edge-dependent average dwell time (AED-ADT) methods that address switching signals, we propose admissible edge-dependent average impulsive interval (AED-AII) to deal with delayed impulses, thereby establishing the relationship between these methods and the decay rate. Meanwhile, a stabilizing controller for discrete impulsive switched linear delayed systems is proposed and the minimum average dwell time and controller gain are obtained. Compared with the previous work, the parameters of Lyapunov functional relation depend on the directed edges; the operation of subsystem is divided into asynchronous time and synchronous time, which are less conservative; the combination of AED-ADT and AED-AII can be applied to a wider range of impulsive switched systems. Finally, two examples are given to show the effectiveness of the results.

Observer-based resilient dynamic event-triggering control for switched systems under DoS and FDI attacks

This article investigates the problem of the observer-based dynamic event-triggering control for networked switched systems under denial-of-service (DoS) attacks and false data injection (FDI) attacks. The considered DoS attack model is limited by duration and frequency, and the FDI attack signal is generated by an exogenous system. First, an extended observer is constructed to estimate both the system state and the FDI attack signal. Subsequently, an observer-based resilient dynamic event-triggered mechanism is designed to reduce communication resource costs and eliminate the limitation of maximum asynchronous times less than dwell time such that the system can frequently switch in the event interval. Furthermore, by employing Lyapunov stability theory and average dwell time method to guarantee the switched system is exponentially stable. Meanwhile, a co-design scheme of controller gains, observer gains, and triggering parameters is developed. Finally, a switched circuit system is used to substantiate the feasibility of the proposed approach.

Dynamic event-triggered-based adaptive fuzzy optimized control for slowly switched nonlinear system with intermittent state constrains

This article presents a novel fuzzy event-triggered optimized strategy for slowly switched nonlinear system using reinforcement learning technique. For addressing intermittent state constraints problem, some improved shifting functions and barrier functions are designed in the adaptive backstepping process. Subsequently, by designing global performance functions with the discount term, the corresponding Hamilton-Jacobi-Bellman equation is derived and the optimal solution can be obtained under critic-actor structure. Different from the existing event-triggered methods, a novel dynamic event-triggered scheme for subsystem is developed, which not only saves communication resources, but also solves the mismatch behaviour between controller and subsystem without restriction on maximum asynchronous intervals and the number of switch within a triggering interval. Furthermore, by using modified average cycle dwell time method and Lyapunov stability theorem, all signals of system are proved to be bounded. Eventually, numerical simulation results validate the superiority of the proposed approach, and this new scheme is applied to single-link robotic manipulator.

Neural-Network-Based Adaptive Fault-Tolerant Cooperative Control of Heterogeneous Multiagent Systems With Multiple Faults and DoS Attacks.

In this article, the issue of adaptive fault-tolerant cooperative control is addressed for heterogeneous multiple unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) with actuator faults and sensor faults under denial-of-service (DoS) attacks. First, a unified control model with actuator faults and sensor faults is developed based on the dynamic models of the UAVs and UGVs. To handle the difficulty introduced by the nonlinear term, a neural-network-based switching-type observer is established to obtain the unmeasured state variables when DoS attacks are active. Then, the fault-tolerant cooperative control scheme is presented by utilizing an adaptive backstepping control algorithm under DoS attacks. According to Lyapunov stability theory and improved average dwell time method by integrating the duration and frequency characteristics of DoS attacks, the stability of the closed-loop system is proved. In addition, all vehicles can track their individual references, while the synchronized tracking errors among vehicles are uniformly ultimately bounded. Finally, simulation studies are given to demonstrate the effectiveness of the proposed method.

Aperiodic sampled‐data stabilization of switched singular systems with asynchronous switching: A hybrid control approach

AbstractThis article investigates the sampled‐data stabilization problem for a class of switched singular systems with aperiodic sampling. The asynchronous switching between the plant and the switched controller caused by sampling is considered. Unlike normal systems, the conventional zero‐order hold type sampled‐data control law may be inapplicable to singular systems. This is because under that control law, the algebraic equations of singular systems may have no solutions at sampling instants. To cope with this problem, a new hybrid control law composed of a mode‐dependent impulsive controller and a mode‐dependent sampled‐data state feedback controller is devised. The impulsive controller adjusts the values of differential substate at sampling instants so that the algebraic equations are solvable. Then, by constructing a novel piecewise sampling‐time‐dependent Lyapunov function and using the average dwell time method as well as convex technique, a sampling‐range‐dependent sufficient condition for exponential stability of the resulting closed‐loop system is established. Moreover, an optimization‐based method is proposed to solve the hybrid controller gains. Simulation results on two examples including a mechanical arm system show the effectiveness of the proposed control method.

Improved input‐to‐state stability criteria for time‐varying switched singular systems

AbstractThis paper is dedicated to proposing improved input‐to‐state stability (ISS) criteria for a class of continuous‐time time‐varying switched singular systems (CTSSS) under slow/fast/slow‐fast switching signals. Specifically, for a CTSSS with time‐varying singular matrices, the authors start with an improved sufficient condition for verifying its ISS under slow switching signals based on the average dwell time method and a relaxed multiple Lyapunov function. Then, considering several or all subsystems may destroy the overall ISS, relaxed sufficient conditions are presented to ensure the ISS of the CTSSS under fast switching signals and slow‐fast switching signals, respectively. Note that the improvement of the proposed ISS criteria is embodied in the derivative of the required multiple Lyapunov functions along with the state trajectories of CTSSS can be positive or negative. Finally, three numerical examples are provided to illustrate the feasibility of the obtained results.

Mean square exponential stability with l2−l∞ gain of discrete-time switched-Markovian jump systems

In this paper, the problem of mean square exponential stability with [Formula: see text] gain is studied for the discrete-time switched-Markovian jump systems, which are composed of a deterministic switched system and a Markovian jump system. The mode-dependent average dwell time method is adopted to design the switching signal for the deterministic switched system, and the Markovian jump property is presented by the Markov chain, which is dependent on the designed mode-dependent average dwell time switching signal. The multiple discontinuous Lyapunov function is constructed to guarantee the mean square exponential stability and [Formula: see text] performance. Furthermore, a novel inequality is established to show the relationship between multiple discontinuous Lyapunov functions and disturbances to derive the [Formula: see text] performance. Finally, two numerical examples and a circuit system are given to demonstrate the effectiveness of the obtained results.

Set‐membership state estimation for delayed switched systems with fading measurement and interval uncertainty

AbstractConsidering the influence of interval uncertainty, a set‐membership state estimation algorithm based on zonotope is proposed for discrete‐time delayed switched systems subject to unknown but bounded noises. To economize on communication resources, an event‐triggered mechanism is introduced to ensure the efficient transmission of the required observation information. For the channel fading phenomenon during data transmission, an interval channel fading model applicable to the zonotope set‐emmbership state estimation is proposed. The asynchronous state observer is constructed by considering the inconsistency between event‐triggered instant and subsystem switched instant. The sufficient conditions for the existence of the state observer are given using the average dwell time method. The optimal observer gain matrix is derived by solving convex optimization. On this basis, the zonotope and the state estimation interval containing states are given by the zonotopic method. Finally, the validity and feasibility of the proposed algorithm are demonstrated by a numerical example with the comparison result.

Exponentially Synchronous Results for Delayed Neural Networks With Leakage Delay via Switched Delay Idea and AED-ADT Method.

Time delay has always been one of the main factors affecting the application performance of neural network (NN) systems, and dynamic performance research of NNs with time delays has been the focus of many scholars in recent years. This article enquires into the exponentially synchronous problem of switched delayed NNs with time delay in the leakage term. Adopting an unusual form from a common switched system, the switching modes of the switched delayed NNs system in this article are dependent on time delays. In the first place, the master, slave, and error NNs models are reconstructed into the switched form by introducing the switched delay idea. Then with the help of the admissible edge-dependent average dwell time (AED-ADT) method and delay-dependent switching adjustment indicators, a novel set of generalized delay-mode-dependent multiple Lyapunov-Krasovskii functionals (MLKFs) is built for analyzing the cases where a state-feedback controller exists and does not exist in the model, and where parts of LKFs may increase during the period when the corresponding subsystems are activated. For these cases, several effective exponential synchronization criteria and switching laws are presented accordingly. At last, the verification of the theoretical results is shown through a few examples.

Asynchronous H∞ output tracking control for uncertain networked switched systems with mode-dependent average dwell time: an event-driven mechanism

This paper considers the problem of event-triggered H ∞ output tracking control for uncertain networked switched systems with both communication constraints and asynchronous switching. A new sampled delay-dependent error tracking uncertain networked switched system is constructed on the basis of event-triggered communication mechanism (ETCM) and the given reference model. By introducing a parameter-dependent Lyapunov–Krasovskii functional and employing the mode-dependent average dwell time (MDADT) method, results on exponential stability and robust H ∞ performance are proposed. Furthermore, the gains of the output tracking controller with matched system mode are obtained by solving a set of linear matrix inequalities (LIMs), at the same time, the parallel results with the mismatched case are also obtained. Simulation results show that the proposed design scheme not only guarantees tracking performance but also saves communication resources effectively.