Dissipative analysis for discrete‐time systems via fault‐tolerant control against actuator failures

This article investigates the problem of robust dissipative fault‐tolerant control for discrete‐time systems with actuator failures. Based on the Lyapunov technique and linear matrix inequality (LMI) approach, a set of delay‐dependent sufficient conditions is developed for achieving the required result. A design scheme for the state‐feedback reliable dissipative controller is established in terms LMIs which can guarantee the asymptotic stability and dissipativity of the resulting closed‐loop system with actuator failures. In addition, the proposed controller not only stabilize the fault‐free system but also to guarantee an acceptable performance of the faulty system. Also as special cases, robust H_∞ control, passivity control, and mixed H_∞ and passivity control with the prescribed performances under given constraints can be obtained for the considered systems. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed fault‐tolerant control technique. © 2016 Wiley Periodicals, Inc. Complexity 21: 579–592, 2016     

不确定时滞系统的时滞相关非脆弱鲁棒[[H_infty]]控制

讨论了不确定时滞系统非脆弱控制器设计问题.利用Lyapunov-Krasovskii稳定性理论和最近建立的积分不等式方法,获得了不确定时滞系统在非脆弱控制器作用下不仅内部渐近稳定,而且具有给定的H∞扰动抑制水平γ的时滞相关条件.然后,针对控制器具有加法不确定性和乘法不确定性两种情况,分别给出了非脆弱控制器的设计方法,这一方法不需要调节参数,利用Matlab的LMI工具箱求解方便,数值仿真实例说明该方法的有效性.     

离散非线性时滞系统的鲁棒耗散控制

针对一类基于T-S模型表示的具有范数有界不确定性离散非线性时滞系统,研究了鲁棒耗散模糊控制问题.对可用T-S模糊模型表示的非线性时滞系统,考虑系统具有范数有界参数不确定性时,应用并行分布式控制方法,得到使得系统稳定且严格耗散的模糊耗散控制器存在的充分性条件.进而通过建立和求解LMI(线性矩阵不等式)约束的凸优化问题,给出了耗散控制律的设计方法.数值算例表明了此方法的可行性和有效性.     

Dissipative sampled‐data control of uncertain nonlinear systems with time‐varying delays

This article investigates the delay‐dependent robust dissipative sampled‐data control problem for a class of uncertain nonlinear systems with both differentiable and non‐differentiable time‐varying delays. The main purpose of this article is to design a retarded robust control law such that the resulting closed‐loop system is strictly (Q, S, R)‐dissipative. By introducing a suitable Lyapunov–Krasovskii functional and using free weighting matrix approach, some sufficient conditions for the solvability of the addressed problem are derived in terms of linear matrix inequalities. From the obtained dissipative result, we deduce four cases namely, H_∞ performance, passivity performance, mixed H_∞, and passivity performance and sector bounded performance of the considered system. From the obtained result, it is concluded that based on the passivity performance it is possible to obtain the controller with less control effort, and also the minimum H_∞ performance and the maximum allowable delay for achieving stabilization conditions can be obtained via the mixed H_∞ and passivity control law. Finally, simulation studies based on aircraft control system are performed to verify the effectiveness of the proposed strategy. © 2015 Wiley Periodicals, Inc. Complexity 21: 142–154, 2016     

Guaranteed Cost Control for a Class of Uncertain Stochastic Impulsive Systems with Markovian Switching

Abstract

This article is concerned with the problem of guaranteed cost control for a class of uncertain stochastic impulsive systems with Markovian switching. To the best of our knowledge, it is the first time that such a problem is investigated for stochastic impulsive systems with Markovian switching. For an uncontrolled system, the conditions in terms of certain linear matrix inequalities (LMIs) are obtained for robust stochastical stability and an upper bound is given for the cost function. For the controlled systems, a set of LMIs is developed to design a linear state feedback controller which can stochastically stabilize the class of systems under study and guarantee the given cost function to have an upper bound. Further, an optimization problem with LMI constraints is formulated to minimize the guaranteed cost of the closed-loop system. Finally, a numerical example is provided to show the effectiveness of the proposed method.     

Resilient dissipative dynamic output feedback control for uncertain Markov jump Lur’e systems with time-varying delays

The resilient dissipative dynamic output feedback control problem for a class of uncertain Markov jump Lur’e systems with piecewise homogeneous transition probabilities and time-varying delays in the discrete-time domain are examined in this study. The designed controller can tolerate additive uncertainties in the controller gain matrix, which result from controller implementations. The time-varying delays are also supposed to be mode-dependent with lower and upper bounds known a priori. By constructing a Lyapunov–Krasovskii functional candidate, the sufficient conditions regarding the existence of desired resilient dissipative controllers are obtained in terms of linear matrix inequalities, thereby ensuring that the resulting closed-loop system is stochastically stable and strictly dissipative. Two numerical examples were established to illustrate the effectiveness of the proposed theoretical results.     

Alternating convex projection methods for discrete-time covariance control design

The problem of designing a controller for a linear, discretetime system is formulated as a problem of designing an appropriate plant-state covariance matrix. Closed-loop stability and multiple-output performance constraints are expressed geometrically as requirements that the covariance matrix lies in the intersection of some specified closed, convex sets in the space of symmetric matrices. We solve a covariance feasibility problem to determine the existence and compute a covariance matrix to satisty assignability and output-norm performance constraints. In addition, we can treat a covariance optimization problem to construct an assignable covariance matrix which satisfies output performance constraints and is as close as possible to a given desired covariance. We can also treat inconsistent constraints, where we look for an assignable covariance which best approximates desired but unachievable output performance objectives; we call this the infeasible covariance optimization problem. All these problems are of a convex nature, and alternating convex projection methods are proposed to solve them, exploiting the geometric formulation of the problem. To this end, analytical expressions for the projections onto the covariance assignability and the output covariance inequality constraint sets are derived. Finally, the problem of designing low-order dynamic controllers using alternating projections is discussed, and a numerical technique using alternating projections is suggested for a solution, although convergence of the algorithm is not guaranteed in this case. A control design example for a fighter aircraft model illustrates the method.This research was completed while the first author was with the Space Systems Control Laboratory at Purdue University. Support from the Army Research Office Grant ARO-29029-EG is gratefully acknowledged.     

HMM-based quantized dissipative control for 2-D Markov jump systems

In this paper, the dissipative quantized control problem is addressed for Markov jump two-dimensional systems based on Roesser model, in which both asynchronous phenomenon and signal quantization between system modes and controller modes are taken into consideration simultaneously. Moreover, the hidden Markov model (HMM) is adopted to tackle such an asynchronous phenomenon. The principal goal is to devise a state feedback controller, which guarantees that the established closed-loop system achieves asymptotic mean square stability as well as satisfies a prescribed extended dissipative property. Drawing support from Lyapunov function approach and inequality technique, some less conservative criteria ensuring the implementability of the desired controller are derived. Ultimately, the availability and practicability of the developed results are certified through a simulation example.     

Quantized stabilization of stochastic systems with multiplicative noise under Markovian switching

A problem of quantized state feedback quadratic mean-square stabilization of discrete-time stochastic processes under Markovian switching and multiplicative noise is considered. A static quantizer is used in the feedback channel and the jump Markovian switching is modeled by a discrete-time Markov chain. The control input is simultaneously applied to both the rate vector and the diffusion term. It is shown that the coarsest quantization density that permits quadratic mean-square stabilization of this system is achieved with the use of a logarithmic quantizer, and the coarsest quantization density is determined by an algebraic Riccati equation, which is also the solution to a special linear stochastic Markovian switching control system. Also, sufficient conditions for exponential mean-square stabilization of such systems are also explored. An example is given to demonstrate the obtained results.     

Observer‐based dissipative control for networked control systems: A switched system approach

This article studies the problem of observer‐based dissipative control problem for wireless networked control systems (NCSs). The packet loss and time delay in the network are modeled by a set of switches, using that a discrete‐time switched system is formulated. First, results for the exponential dissipativity of discrete‐time switched system with time‐varying delays are proposed by using the average dwell time approach and multiple Lyapunov–Krasovskii function. Then, the results are extended to drive the controller design for considered wireless NCS. The attention is focused on designing an observer‐based state feedback controller which ensures that, for all network‐induced delay and packet loss, the resulting error system is exponentially stable and strictly dissipative. The sufficient conditions for existence of controllers are formulated in the form of linear matrix inequalities (LMIs), which can be easily solved using some standard numerical packages. Both observer and controller gains can be obtained by the solutions of set of LMIs. Finally, numerical examples are provided to illustrate the applicability and effectiveness of the proposed method. © 2014 Wiley Periodicals, Inc. Complexity 21: 297–308, 2015     

GUARANTEED COST CONTROL OF CONTINUOUS-TIME UNCERTAIN SINGULAR SYSTEM WITH BOTH STATE AND INPUT DELAYS

The guaranteed cost control problem for a continuous-time uncertain singular system with state and control delays, and a given quadratic cost function is studied in this paper. Sufficient conditions for the existence of the guaranteed cost controller are derived based on the linear inequality (LMI) approach. A parameterized characterization of the guaranteed cost laws is given in terms of the feasible solutions to a certain LMI, and the cost function of guaranteed cost controller exists an upper bound.     

Robust reliable dissipative control of nonlinear networked control systems

This article focuses on the robust reliable dissipative control issue for a class of switched discrete‐time nonlinear networked control systems with external energy bounded disturbances. In particular, nonlinearities are modeled in a probabilistic way according to Bernoulli distributed white sequence with known conditional probability. A Lyapunov–Krasovskii functional is proposed based on which sufficient conditions for the existence of the reliable dissipative controller are derived in terms of linear matrix inequalities (LMIs) which ensures exponentially stability as well as dissipative performance of the resulting closed‐loop system. The explicit expression of the desired controller gains can be obtained by solving the established LMIs. Finally, a numerical example is presented to demonstrate the effectiveness and applicability of the proposed design strategy. © 2016 Wiley Periodicals, Inc. Complexity 21: 427–437, 2016     

Characterization and computation of control invariant sets for linear impulsive control systems

Impulsive control systems are suitable to describe and control a venue of real-life problems, going from disease treatment to aerospace guidance. The main characteristic of such systems is that they evolve freely in-between impulsive actions, which makes it difficult to guarantee its permanence in a given state-space region. In this work, we develop a method for characterizing and computing approximations to the maximal control invariant sets for linear impulsive control systems, which can be explicitly used to formulate a set-based model predictive controller. We approach this task using a tractable and non-conservative characterization of the admissible state sets, namely the states whose free response remains within given constraints, emerging from a spectrahedron representation of such sets for systems with rational eigenvalues. The so-obtained impulsive control invariant set is then explicitly used as a terminal set of a predictive controller, which guarantees the feasibly asymptotic convergence to a target set containing the invariant set. Necessary conditions under which an arbitrary target set contains an impulsive control invariant set (and moreover, an impulsive control equilibrium set) are also provided, while the controller performance are tested by means of two simulation examples.     

LMI Optimization Approach to Synchronization of Stochastic Delayed Discrete-Time Complex Networks

Complex networks are widespread in real-world systems of engineering, physics, biology, and sociology. This paper is concerned with the problem of synchronization for stochastic discrete-time drive-response networks. A dynamic feedback controller has been proposed to achieve the goal of the paper. Then, based on the Lyapunov second method and LMI (linear matrix inequality) optimization approach, a delay-independent stability criterion is established that guarantees the asymptotical mean-square synchronization of two identical delayed networks with stochastic disturbances. The criterion is expressed in terms of LMIs, which can be easily solved by various convex optimization algorithms. Finally, two numerical examples are given to illustrate the proposed method.     

Small-gain technique-based adaptive output constrained control design of switched networked nonlinear systems via event-triggered communications

This paper investigates the problem of event-triggered tracking control for switched networked nonlinear systems with asymmetric time-varying output constraints. To handle the output constraints, an output-dependent generic constraint function is constructed to describe relationship between the output and the performance requirement. Meanwhile, an event-triggering rule is designed to reduce communication frequency between the controller and the actuator, thereby reducing the burden of the network communication. Based on the common Lyapunov function method and event-triggered control strategy, an adaptive control method is designed, which can guarantee that the closed-loop signals are bounded and avoid the Zeno behavior. Different from existing results considering constraints, the proposed scheme not only relaxes the restricted condition of constraint boundaries but also both the cases with and without output constraints can be addressed simultaneously. Furthermore, the stability of the system can be guaranteed by the small-gain technique. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed scheme.     

Stabilizability of a class of stochastic bilinear hybrid systems

The problem of the stabilizability of stochastic nonlinear hybrid systems with a Markovian or any switching rule is considered. Using the Lyapunov technique sufficient conditions for the asymptotic stabilizability in probability by a smooth controller in every structure are found. In particular, the asymptotic stabilizability in probability problem of stochastic bilinear hybrid systems with a Markovian or any switching rule is discussed and a closed-loop controller is found. Also the sufficient conditions for the exponential mean-square stabilizability for bilinear hybrid systems with any switching based on the Lie algebra approach are formulated and an open-loop controller is designed. The obtained results are illustrated by examples and simulations.     

Passivity-based control for Hopfield neural networks using convex representation

This paper considers the problem of passivity-based controller design for Hopfield neural networks. By making use of a convex representation of nonlinearities, a feedback control scheme based on passivity and Lyapunov theory is presented. A criterion for existence of the controller is given in terms of linear matrix inequality (LMI), which can be easily solved by a convex optimization problem. An example and its numerical simulation are given to show the effectiveness of the proposed method.     

A hierarchical structure of observer-based adaptive fuzzy-neural controller for MIMO systems

An observer-based adaptive controller developed from a hierarchical fuzzy-neural network (HFNN) is employed to solve the controller time-delay problem for a class of multi-input multi-output (MIMO) non-affine nonlinear systems under the constraint that only system outputs are available for measurement. By using the implicit function theorem and Taylor series expansion, the observer-based control law and the weight update law of the HFNN adaptive controller are derived. According to the design of the HFNN hierarchical fuzzy-neural network, the observer-based adaptive controller can alleviate the online computation burden. Moreover, the common adaptive controller is utilized to control all the MIMO subsystems. Hence, the number of adjusted parameters of the HFNN can be further reduced. In this paper, we prove that the proposed observer-based adaptive controller can guarantee that all signals involved are bounded and that the outputs of the closed-loop system track asymptotically the desired output trajectories.     

DELAY DEPENDENT ROBUST DISSIPATIVE CONTROL FOR A CLASS OF NONLINEAR TIME-DELAY SYSTEMS

We discuss the delay dependent robust dissipative problem for a class of time-delay systems with nonlinear perturbations. And the sufficient conditions for the delay dependent robust dissipation and quadratic stability are given by the linear matrix inequalities (LMIs), then the time-delay bound and the delay dependent robust dissipative state feedback controller are presented.     

Robust reliable stabilization of uncertain switched neutral systems with delayed switching

This paper investigates the problem of robust reliable control for a class of uncertain switched neutral systems under asynchronous switching, where the switching instants of the controller experience delays with respect to those of the system and the parameter uncertainties are assumed to be norm-bounded. A state feedback controller is proposed to guarantee exponential stability and reliability for switched neutral systems, and the dwell time approach is utilized for the stability analysis and controller design. A numerical example is given to illustrate the effectiveness of the proposed method.