Quantized control for networked switched systems under denial-of-service attacks via a barrier event-triggered mechanism

This paper studies the quantized control problem for networked switched systems (NSSs) under denial-of-service (DoS) attacks. The quantized state information, together with the switching signal, is transmitted to the controller through a network. In order to reduce communication consumption and controller update frequency, a barrier event-triggered mechanism is utilized to monitor the state at discrete time. Because of the event-triggered mechanism and the DoS attacks on the network, the mismatch between the system mode and the controller mode is thus frequently encountered, which may lead to quantization saturation and system instability. To solve the problem, an update rule is presented for the dynamic quantizer by switching between zooming in and zooming out of the zooming variable, and a feedback controller is proposed with a jointly designed event-triggered mechanism and a dynamic quantizer. Sufficient conditions on the constraints of DoS frequency and duration are obtained to ensure the exponential stability of the switched system. The effectiveness of the obtained results is illustrated by simulation examples and comparative studies.     

Stabilization of switched linear systems using an improved event-triggered control scheme

This paper is concerned with the event-triggered control of switched linear systems. The coupling of system switching and event-triggered communication raises two phenomena: (1) the update of controller cannot always catch up with the active subsystem; (2) the switching may lead to additional triggers. The first phenomenon is called the asynchronous switching induced by network communication and the second one brings great difficulty to avoid the Zeno behavior of event-triggered mechanism (ETM). To address the above problem, we propose a new ETM which contains the switching signal of models and controllers and the discontinuity of triggering error at switching time instants. A relative threshold strategy, combined with a jump function, is designed as a new threshold function. By introducing a compensation term, the linear feedback control law is extended to avoid the Zeno behavior of ETM and improve the solvability of control algorithm. Based on the proposed event-triggered control scheme, the exponential stabilization of switched systems is achieved with relaxed constraints on the triggering and switching conditions. The obtained results are validated by a numerical example.     

Model matching of input/state switched asynchronous sequential machines with the external switching signal

This article investigates the input/state model matching problem of switched asynchronous sequential machines (ASMs) with the external switching signal in the framework of corrective control theory. The considered switched ASM is governed by the external switching signal that arbitrarily changes the mode of the switched ASM, prompting the active submachine into unpredictable state drift. We address the existence condition and design procedure for a proper corrective controller that matches the stable-state behavior of the closed-loop system to that of a reference model under any switching sequence. An illustrative example is provided for demonstrating the synthesis procedure of the proposed corrective controller. Compared with the prior work, the subject of this study is more challenging since rather than manipulated in favor of attaining model matching, the switching signal inflicts adversarial dynamic constraint that must be overcome by the controller.     

Switching design for suboptimal guaranteed cost control of 2-D nonlinear switched systems in the Roesser model

This paper deals with the problem of switching design for guaranteed cost control of discrete-time two-dimensional (2-D) nonlinear switched systems described by the Roesser model. The switching signal, which determines the active mode of the system, is subject to a state-dependent process whose values belong to a finite index set. By using 2-D common Lyapunov function approach, a sufficient condition expressed in terms of tractable matrix inequalities is first established to design a min-projection switching rule that makes the 2-D switched system asymptotically stable. The obtained result on stability analysis is then utilized to synthesize a suboptimal state feedback controller that minimizes the upper bound of a given infinite-horizon cost function. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design method.     

Data-driven optimal tracking control of switched linear systems

This paper addresses the optimal tracking control for switched linear systems with unknown dynamics. We convert the problem into an optimal control problem of the augmented switched systems. In view of the augmented systems, we propose a data-driven switched linear quadratic regular algorithm for obtaining the optimal switching signal under unknown system dynamics. It is proved that the optimal switching signal will not cause Zeno behavior and can make the system stable. Besides, with the proposed algorithm, we just need to identify an autonomous system instead of the original systems, which has fewer parameters to be determined. A numerical example is given to illustrate the validity of the main results.     

Adaptive-observer-based output-constrained tracking of a class of arbitrarily switched uncertain non-affine nonlinear systems

This paper addresses an adaptive output-feedback tracking problem of arbitrarily switched pure-feedback nonlinear systems with time-varying output constraints and unknown control directions. In this work, the tracking problem of switched non-affine nonlinear systems with output constraints is transformed into the stabilization problem of switched unconstrained affine systems. The main contribution of this paper is to present a universal formula for constructing an adaptive state-observer-based tracking controller with only two adaptive parameters by using the common Lyapunov function method. These adaptive parameters in the proposed control scheme are derived using the function approximation technique and a priori knowledge of the signs of control gain functions is not required. The theoretical analysis is presented for the Lyapunov stability and the constraint satisfaction of the resulting closed-loop system in the presence of arbitrary switchings.     

Controllability of switched time-delay systems under constrained switching

Different from the existing mathematical models for switched systems, where the switching from one subsystem to another subsystem is finished instantly, in this paper it is assumed that the switching is a transfer process. Moreover, there exists a basic transfer subsystem such that in the transfer process, the transfer subsystem is active. Based on the model of switched systems under constrained switching, this paper studies the controllability of such systems with time delay in the control function. A necessary and sufficient condition for controllability of such systems is established. Finally, an example is given to illustrate the utility of our results.     

一类线性系统的数值控制设计

主要讨论了具有不稳定切换子模型的切换线性系统的稳定性问题.首先考虑了通过设计切换律来达到切换线性系统的稳定性问题.然后研究了切换线性控制系统可镇定性问题,通过设计控制律和切换律得到系统可镇定的判据.     

Distributed adaptive switching consensus control of heterogeneous multi-agent systems with switched leader dynamics

In this paper, the leader-following distributed consensus control problem is addressed for general linear multi-agent systems with heterogeneous uncertain agent dynamics and switched leader dynamics. Different from most existing results with a single linear time-invariant (LTI) leader dynamics, the leader dynamics under consideration is composed by a family of LTI models and a switching logic governing the switches among them, which is capable of generating more diverse and sophisticated reference signals to accommodate more complicated consensus control design tasks. A novel distributed adaptive switching consensus protocol is developed by incorporating the model reference adaptive control mechanism and arbitrary switching control technique, which can be synthesized by following a two-layer hierarchical design scheme. A numerical example has been used to demonstrate the effectiveness of the proposed approach.     

A new method for control of nonlinear state-dependent switched systems

In this paper, a new method for the control of input-affine nonlinear switched systems is introduced. The system switching conditions are assumed to be state-dependent, rather than the simpler input-dependent case. The main contribution of this research is that the effects of switched dynamics are interpreted as a model uncertainty bounded within a polynomial of states norms, with unknown coefficients. In order to prevent extra conservativeness, coefficients are tuned adaptively, so that a minimal state-varying bound could be achieved. This is unlike the conventional sliding mode control (SMC) scheme, where the existence of a constant and usually large upper bound must be presumed. To address the challenge of coping with such a new concept of uncertainty, an extended form of the original adaptive fuzzy sliding mode control scheme is proposed. Adaptation laws are used to tune a fuzzy controller and also real-time estimation of the instantaneous bound of uncertainties. Closed-loop stability is guaranteed by proposing a group of multiple Lyapunov functions (MLF) with tunable parameters. Except for the mild condition that the largest difference between the magnitudes of the sub-manifolds of the switched system is bounded by a polynomial of states with uncertain coefficients, the proposed method has the distinct advantage that no information about the dynamic equations or switching conditions is required in the control design stage. The proposed method is applied to the two challenging case studies, depicting the outstanding effectiveness of the method.     

Identification of switched linear systems using subspace and integer programming techniques

We consider the identification of a switched linear system which consists of linear sub-models, with a rule that orchestrates the switching mechanism between the sub-models. Taking a set of switched linear systems and using a state space framework, we show that it is possible to combine subspace methods with mixed integer programming for system identification. The states of the system are first extracted from input–output data using sub-space methods. Once the state variables are known, the switched system is re-written as a mixed logical dynamical (MLD) system and the model parameters are calculated for via mixed integer programming. We report an example at the end of this paper together with simulation results in the presence of noise.     

多时滞线性切换系统的H_∞控制

研究了连续的多时滞线性切换系统的H_∞控制问题,用Lyapunov函数和凸组合技术,给出了连续的多时滞切换系统满足H_∞性能指标的充分条件和切换律的设计方案,并且进一步讨论了离散的多时滞线性切换系统的H_∞控制问题.     

Hybrid observer design for linear switched system via Differential Petri Nets

The aim of this paper is to propose a hybrid observer design for linear switched systems modelled either via Differential Petri Nets (DPN) or via Timed Differential Petri Nets (TDPN). The switched systems, herein, considered are characterized by switching laws that can depend on the continuous states or on both of a given dwell time and the continuous states. In addition, the structure of the proposed observers is based on a discrete observer and a continuous observer on interaction. The discrete observer reconstructs the discrete mode, by estimating both of the discrete marking and the firing vector. Once, the active mode is obtained, the continuous states are estimated. Finally, the outputs of the continuous observer are used to update the marking and the firing vector. At the end of the paper, several simulation results are presented to illustrate the proposed approach.     

A parameter estimation scheme for a class of sequential hybrid systems

It may happen that the equations governing the response of dynamical systems have some parameters whose values may not be known a priori and have to be obtained using parameter estimation schemes. In this article, we present a parameter estimation scheme for a class of sequential hybrid systems. By hybrid systems, we refer to those systems whose response is described by different governing equations corresponding to various regimes/modes of operation along with some criteria to switch between the same. In a sequential hybrid system, the different modes are arranged in a specific sequence and the system can switch from a given mode to either the previous mode or the following mode in this sequence. Here, we consider those systems whose governing equations consist of ordinary differential equations and algebraic equations. The conditions for switching between the various modes (referred to as transition conditions) are in the form of linear inequalities involving the system output. We shall first consider the case where the transition conditions are known completely. We present a parameter update scheme along with sufficient conditions that will guarantee bounded parameter estimation errors. Then, we shall consider the case where the transition conditions are not known in the sense that some parameters in these conditions are not known. We present a parameter estimation scheme for this case. We illustrate the performance of the parameter estimation scheme in both cases with some examples.     

Stabilization of switched linear systems with time-delay in detection of switching signal

A feedback stabilization problem for switched linear systems with time-delay in detection of switching signal is formulated. First, online state feedback controller design method for asymptotic stability and exponential stability is given. Then, offline state feedback controller design method for asymptotic stability and exponential stability is given as well.     

Adaptive fuzzy backstepping control for a class of MIMO switched nonlinear systems with unknown control directions

In this article, an adaptive fuzzy output tracking control approach is proposed for a class of multiple‐input and multiple‐output uncertain switched nonlinear systems with unknown control directions and under arbitrary switchings. In the control design, fuzzy logic systems are used to identify the unknown switched nonlinear systems. A Nussbaum gain function is introduced into the control design and the unknown control direction problem is solved. Under the framework of the backstepping control design, fuzzy adaptive control and common Lyapunov function stability theory, a new adaptive fuzzy output tracking control method is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed‐loop system are bounded and the tracking error remains an adjustable neighborhood of the origin. A numerical example is provided to illustrate the effectiveness of the proposed approach. © 2015 Wiley Periodicals, Inc. Complexity 21: 155–166, 2016     

Stabilization of switched DAEs via fast switching

Switched differential algebraic equations (switched DAEs) can model dynamical systems with state constraints together with sudden structural changes (switches). These switches may lead to induced jumps and can destabilize the system even in the case that each mode is stable. However, the opposite effect is also possible; in particular, the question of finding a stabilizing switching signal is of interest. Two approaches are presented how to stabilize a switched DAE via fast switching. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

H∞ performance for uncertain discrete switched systems with interval time-varying delay via switching signal design

The switching signal design for H_∞ performance of uncertain discrete switched systems with interval delay and linear fractional perturbations is considered in this paper. Some LMI stability criteria are proposed to design the switching signal and guarantee the H_∞ performance for discrete switched time-delay system. Some nonnegative inequalities are introduced to improve the conservativeness of the proposed results. A numerical example is illustrated to show the less conservativeness of the main result. Finally, a water quality model is also provided to demonstrate the practical applications of our proposed results.     

Stability analysis of switched ARX models and application to learning with guarantees

The main subject of this work is the stability analysis of Switched Auto-Regressive models with eXogenous inputs (SARX), which constitute a reference class for switched and hybrid system identification. The work introduces novel conditions for the arbitrary switching stability of multiple-input multiple-output SARX models which exploit the peculiar structure of their state-space realization. The analysis relies on the properties of block companion matrices, and partly leverages results from the theory of non-negative matrices, without nevertheless asking for an input–output positive behavior of the model. The novel stability conditions have a simple formulation in terms of linear co-positive common Lyapunov functions, and come at a remarkably low computational cost, being solvable by Linear Programming. The low computational burden is particularly attractive in an identification context, as it allows to efficiently constrain learning procedures in order to obtain SARX models with stability guarantees. The latter is itself a contribution of the work, as it fills a gap in the literature on the estimation of SARX models. The results are validated on a particular learning technique based on Regression Trees – a well known machine learning algorithm – which has shown remarkable accuracy in experimental environments.     

On stability of discrete-time switched systems

This article deals with stability of discrete-time switched systems. Given a family of nonlinear systems and the admissible switches among the systems in the family, we first propose a class of switching signals under which the resulting switched system is globally asymptotically stable. We allow unstable systems in the family and our stability condition depends solely on asymptotic behaviour of the switching signals. We then discuss algorithmic construction of the above class of switching signals, and show that in the presence of exogenous inputs and outputs, a switching signal so constructed also ensures input/output-to-state stability for discrete-time switched nonlinear systems. We finally show that our class of switching signals that ensures global asymptotic stability also extends to the continuous-time setting with minor modifications under standard assumptions. We employ multiple Lyapunov-like functions and graph theoretic tools as the main apparatuses for our analysis.