Quantized stabilization of switched systems with switching delays and packet loss

This paper is concerned with the problem of designing an observer-based quantized feedback controller for the continuous-time switched linear systems, in which the transmission of switching signal is subject to unbounded delays and packet loss. To deal with the unbounded switching delays, we design a constant $\overline{d}$ to determine that the switching signal received by controller is ignored or not. Based on that, if the signal is timestamped, the controller’s mode is uniquely determined. Moreover, we adjust the quantizer parameters in real time depending on the actual transmission situations to ensure the unsaturation of quantizer and thus the boundness of quantization error. Within this setup, we derive a maximum allowable packet loss rate ensuring the mean square stability of the closed-loop switched systems. An illustrative example is given to show the usefulness of the proposed framework for the quantized stabilization of some classes of switched systems.     

Data-driven adaptive optimal control of linear uncertain systems with unknown jumping dynamics

This paper focuses on the optimal control of a DC torque motor servo system which represents a class of continuous-time linear uncertain systems with unknown jumping internal dynamics. A data-driven adaptive optimal control strategy based on the integration of adaptive dynamic programming (ADP) and switching control is presented to minimize a predefined cost function. This takes the first step to develop switching ADP methods and extend the application of ADP to time-varying systems. Moreover, an analytical method to give the initial stabilizing controller for policy iteration ADP is proposed. It is shown that under the proposed adaptive optimal control law, the closed-loop switched system is asymptotically stable at the origin. The effectiveness of the strategy is validated via simulations on the DC motor system model.     

Asynchronous switching for switched nonlinear input delay systems with unstable subsystems

We study the input-to-state stability (ISS) of switched nonlinear input delay systems under asynchronous switching. Our results apply to cases where some subsystems of the switched systems are not necessarily stable under the influence of input delay. By making a compromise among the matched-stable period, the matched-unstable period, and the unmatched period and allowing the increase of the Lyapunov–Krasovskii functional (LKF) on all the switching times, the extended stability criteria for switched delay systems in generally nonlinear setting are derived first. Then, we focus on switched nonlinear input delay systems where the presence of the input delay leads to the instability of some subsystems of it. By explicitly constructing input-to-state stable LKF, the sufficient conditions for ISS of switched nonlinear input delay systems under asynchronous switching are presented. Finally, two examples are given to illustrate the effectiveness of the proposed theory.     

Sampled-data control of a class of switched nonlinear systems under asynchronous switching

This paper focuses on an output feedback stabilization problem for a class of switched nonlinear systems in non-strict feedback form under asynchronous switching via sampled-data control. Since the output of the considered systems is measurable only at the sampling instants, an observer is designed with a tunable scaling gain to estimate the state, and then a sampled-data controller is constructed with the sampled estimated state. As a distinctive feature, a merging virtual switching signal is introduced to describe the asynchronous switching generated by detecting the activation of the subsystem. By choosing an appropriate Lyapunov function, it is proved that the constructed controller with dwell time constraint can globally stabilize the considered systems under asynchronous switching. Finally, the effectiveness of the proposed method is illustrated by two examples.     

Stabilization of discrete-time switched singular systems with state,output and switching delays

This paper is concerned with state feedback stabilization of discrete-time switched singular systems with time-varying delays existing simultaneously in the state, the output and the switching signal of the switched controller. On the basis of equivalent dynamics decomposition and Lyapunov–Krasovskii method, exponential estimates for the response of slow states of the closed-loop subsystems running in asynchronous and synchronous periods are first given. Exponential estimates for the response of fast states are also provided by establishing an analytic equation to solve the fast states and using some algebraic techniques. Then, by employing the obtained exponential estimates and the piecewise Lyapunov function approach with average dwell time (ADT) switching, sufficient conditions for the existence of a class of stabilizing switching signals and state feedback gains are derived, which explicitly depend on upper bounds on the delays and a lower bound on the ADT. Finally, two numerical examples are provided to illustrate the effectiveness of the obtained theoretical results.     

Data-driven optimal tracking control for discrete-time systems with delays using adaptive dynamic programming

In this paper, the data-driven adaptive dynamic programming (ADP) algorithm is proposed to deal with the optimal tracking problem for the general discrete-time (DT) systems with delays for the first time. The model-free ADP algorithm is presented by using only the system’s input, output and the reference trajectory of the finite steps of historical data. First, the augmented state equation is constructed based on the time-delay system and the reference system. Second, a novel data-driven state equation is derived by virtue of the history data composed of input, output and reference trajectory, which is considered as a state estimator.Then, a novel data-driven Bellman equation for the linear quadratic tracking (LQT) problem with delays is deduced. Finally, the data-driven ADP algorithm is designed to solve the LQT problem with delays and does not require any system dynamics. The simulation result demonstrates the validity of the proposed data-driven ADP algorithm in this paper for the LQT problem with delays.     

Stability and L2-gain analysis of switched input delay systems with unstable modes under asynchronous switching

We consider the stability and L₂-gain analysis problem for a class of switched linear systems. We study the effects of the presences of input delay and switched delay in the feedback channels of the switched linear systems with an external disturbance. By contrast with the most of the contributions available in literatures, we do not require that all the modes of the switched system are stable when input delay appears in the feedback input. By reaching a compromise among the matched-stable period, the matched-unstable period, and the unmatched period and permitting the increasing of the multiple Lyapunov functionals on all the switching times, the solvable conditions of exponential stability and weighted L₂-gain are developed for the switched system under mode-dependent average dwell time scheme (MDADT). Finally, numerical examples are given to illustrate the effectiveness of the proposed theory.     

Robust simultaneous fault detection and control for a class of nonlinear stochastic switched delay systems under asynchronous switching

This paper concerns the simultaneous fault detection and control (SFDC) problem for a class of nonlinear stochastic switched systems with time-varying state delay and parameter uncertainties. The switching signal of detector/controller unit (DCU) is assumed to be with switching delay, which results in the asynchronous switching between the subsystems and DCU. By constructing a switching strategy depending on the state and switching delays, new sufficient conditions expressed by a set of linear matrix inequalities (LMIs) is derived to design DCU gains. This problem is formulated as an H_∞ optimization problem and both mean square exponential stability and fault detection of augmented system are considered. A numerical example is finally exploited to verify the effectiveness and potential of the achieved scheme.     

Model reference adaptive control for switched linear systems using switched multiple models control strategy

In this paper, the multiple model strategy is applied to the adaptive control of switched linear systems to improve the transient performance. The solvability of the adaptive stabilization problem of each subsystem is not required. Firstly, the two-layer switching mechanism is designed. The state-dependent switching law with dwell time constraint is designed in the outer-layer switching to guarantee the stability of the switched systems. During the interval of dwell time constraint, the parameter resetting adaptive laws are designed in the inner-layer switching to improve the transient performance. Secondly, the minimum dwell time constraint providing enough time for multiple model adaptive control strategy to work fully and maintaining the stability of the switched systems is found. Finally, the proposed switched multiple model adaptive control strategy guarantees that all the closed-loop system signals remain bounded and the state tracking error converges to zero.     

Asynchronous input-output finite-time filtering for switched LPV systems

The input-output finite-time filtering problem is addressed for a class of switched linear parameter-varying systems in this paper. Firstly, by constructing a parameter-dependent Lyapunov function and resorting to the average dwell time approach, sufficient conditions ensuring finite-time boundedness and input-output finite-time stability are established for the augmented filtering error system. Then, a parameter-dependent asynchronous filter is designed such that the augmented filtering error system are both finite-time bounded and input-output finite-time stable. Finally, the active magnetic bearing model is introduced and verifies the main algorithms in this paper.     

Stabilization of switched linear singular systems with state reset

This paper investigates the stability and stabilization of switched linear singular systems with state reset at switching instants. Based on the dynamics decomposition of singular subsystems, a sufficient stability condition for the system with the given state reset is obtained. Then, the stabilization problem by state reset is investigated and an algorithm for computing the reset matrices is presented. The obtained results extend some previous works on both singular switched systems and reset control for normal switched systems. Finally, a numerical example is presented to illustrate the effectiveness of the proposed approach.     

Non-fragile dissipative filtering for 2-D switched systems

This paper investigates the non-fragile dissipative filtering problem for a class of two-dimensional (2-D) switched systems. Based on the well-known Roesser model, a 2-D switched system is considered. A stochastic process subject to a so-called sojourn probability is utilized as the switching rule. The non-fragile concept is introduced to design the filter in which the additive gain variation is assumed to occur randomly. Sufficient conditions for the existence of a desired dissipative filter are presented and the design scheme is given by convex optimization techniques. A numerical example is provided to show the effectiveness and the superiority of the proposed new design technique.     

Finite-time stabilization of a class of upper-triangular switched nonlinear systems

This paper investigates the finite-time stabilization for a class of upper-triangular switched nonlinear systems, where nonlinearities are allowed to be lower-order growing. Due to the special structure of the considered system, the presented methods for lower-triangular switched nonlinear systems in the literature can not be directly utilized. To solve the problem, a state feedback control law with a new structure is designed to guarantee the global finite-time stability of the closed-loop system under arbitrary switching signals by using the recursive design approach and the nested saturation method. A simulation example is provided to show the effectiveness of the proposed method.     

Fault-tolerant safe control design of switched and interconnected nonlinear systems

This paper provides novel fault-tolerant safe control (FTSC) strategies for switched and interconnected nonlinear systems. With several switching and interconnection situations considered, the proposed corresponding strategies ensure that the state never enters the unsafe set and asymptotically converges to the origin in the presence of faults. This relies on a proposed concept named “fault-tolerant control Lyapunov-Barrier functions (FTCLBF)”. Two practical examples are taken to demonstrate the efficiency of the proposed method.     

Adaptive fuzzy tracking control for switched uncertain strict-feedback nonlinear systems

This paper concerns an adaptive fuzzy tracking control problem for a class of switched uncertain nonlinear systems in strict-feedback form via the modified backstepping technique. The unknown nonlinear functions are approximated by the generalized fuzzy hyperbolic model (GFHM). It is shown that if the designed parameters in the controller and adaptive laws are appropriately selected, then all closed-loop signals are bounded and the stability of the system can be kept under average dwell time methods. In the end, simulation studies are presented to illustrate the effectiveness of the proposed method.     

Event-triggered sliding mode control of uncertain switched systems under denial-of-service attacks

This study is concerned with the event-triggered sliding mode control problem for a class of cyber-physical switched systems, in which the Denial-of-Service (DoS) attacks may randomly occur according to the Bernoulli distribution. A key issue is how to design the output feedback sliding mode control (SMC) law for guaranteeing the dynamical performance of the closed-loop system under DoS attacks. To this end, an event-triggered mechanism is firstly introduced to reduce the communication load, under which the measurement signal is transmitted only when a certain triggering condition is satisfied. An usable output signal for the controller is constructed to compensate the effect of unmeasured states and DoS attacks. And then, a dynamic output feedback sliding mode controller is designed by means of the attack probability and the compensated output signals. Both the reachability and the mean-square exponential stability of sliding mode dynamics are investigated and the corresponding sufficient conditions are obtained. Finally, some numerical simulation results are provided.     

Output reachable set estimation for discrete-time switched systems with persistent dwell-time

This paper is concerned with the output reachable set estimation for discrete-time switched systems. The switching signal is considered as persistent dwell-time (PDT), which is more general and flexible compared with the common dwell-time and average dwell-time switching. The estimation of output reachable set is determined by a collection of bounding ellipsoids based on a family of quasi-time-dependent (QTD) Lyapunov functions. Furthermore, a set of non-fragile QTD controllers is designed. Finally, two examples are employed to illustrate the potentials of proposed methods.     

Finite-time asynchronous filtering for switched linear systems with an event-triggered mechanism

This paper investigates the event-triggered finite-time H_∞ filtering for a class of continuous-time switched linear systems. Considering that the system may switch within an inter-event interval, the asynchronous problem is taken into account for the system and filter modes. By adopting the average dwell time (ADT) technique and multiple Lyapunov functions, new conditions are obtained to guarantee that the filtering error system is finite-time bounded with a prescribed disturbance attenuation performance. Further, the finite-time H_∞ filter together with event-triggered mechanism is co-designed for the switched linear systems. Finally, a numerical example is provided to demonstrate the effectiveness of the method proposed in this paper.     

Adaptive practical finite-time stabilization for switched nonlinear systems in pure-feedback form

This paper investigates adaptive practical finite-time stabilization for a class of switched nonlinear systems in pure-feedback form. Under some appropriate assumptions, a controller and adaptive laws are designed by using adding a power integrator technique, and neural networks are employed to approximate unknown nonlinear functions. It is proved that all states of the closed-loop system converge to a small neighborhood of the origin in finite time. Finally, two simulations are provided to show the feasibility and validity of the proposed control scheme.