Cooperative containment of discrete‐time linear multi‐agent systems

This paper investigates the cooperative containment control problem for discrete‐time multi‐agent systems with general linear dynamics. Distributed containment control protocols on the basis of state feedback design and output feedback design are proposed. Necessary and sufficient conditions are presented for both the state feedback and output feedback cases, which are less conservative than those in the literature. These conditions depend on the spectral properties of the topology matrix. Then, effective algorithms are proposed to obtain control gain matrices for both cases based on H _∞ type Riccati design. Simulation examples are provided finally to demonstrate the effectiveness of the proposed design methods. Copyright © 2013 John Wiley & Sons, Ltd.     

Reachable set estimation for discrete‐time linear systems with time delays

This paper is concerned with the reachable set estimation problem for discrete‐time linear systems with multiple constant delays and bounded peak inputs. The objective is to check whether there exists a bounded set that contains all the system states under zero initial conditions. First, delay‐dependent conditions for the solvability of the addressed problem are derived by employing a novel Lyapunov–Krasovskii functional. The obtained conditions are expressed in terms of matrix inequalities, which are linear when only one scalar variable is fixed. On the basis of these conditions, an ellipsoid containing the reachable set of the considered system is obtained. An approach for determining the smallest ellipsoid is also provided. Second, the approach and results developed in the first stage are generalized to the case of systems with polytopic parameter uncertainties, and delay‐dependent conditions are given in the form of relaxed matrix inequalities. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed methods. Copyright © 2013 John Wiley & Sons, Ltd.     

H∞ model predictive control for constrained discrete‐time piecewise affine systems

This paper investigates stability analysis for piecewise affine (PWA) systems and specifically contributes a new robust model predictive control strategy for PWA systems in the presence of constraints on the states and inputs and with l₂ or norm‐bounded disturbances. The proposed controller is based on piecewise quadratic Lyapunov functions. The problem of minimization of the cost function for model predictive control design is changed to minimization of the worst case of the cost function. Then, this objective is reduced to minimization of a supremum of the cost function subject to a terminal inequality by considering the induced l₂‐norm. Finally, the predictive controller design problem is turned into a linear matrix inequality feasibility exercise with constraints on the input signal and state variables. It is shown that the closed‐loop system is asymptotically stable with guaranteed robust performance. The validity of the proposed method is verified through 3 well‐known examples of PWA systems. Simulation results are provided to show good convergence properties along with capability of the proposed controller to reject disturbances.     

IQC‐based robustness analysis of discrete‐time linear time‐varying systems

The paper investigates the robust stability and performance of uncertain linear time‐varying (LTV) systems using an integral quadratic constraint (IQC) based analysis approach. Specifically, previous theoretical work on IQC‐based robustness analysis of linear time‐invariant (LTI) systems is extended to discrete‐time LTV systems. In the case of a general LTV nominal system, the analysis solution is provided in terms of an infinite‐dimensional convex optimization problem. This optimization problem reduces into a finite‐dimensional semidefinite program when the nominal system in question is finite horizon, periodic, or, more generally, eventually periodic. Finally, the results are applied to an unmanned aircraft control system executing an aggressive maneuver, where the developed techniques are used to find the region in which the aircraft is guaranteed to reside at the end of its planned trajectory. Copyright © 2017 John Wiley & Sons, Ltd.     

Robust state‐feedback control of stochastic state‐multiplicative discrete‐time linear switched systems with dwell time

Linear discrete‐time switched stochastic systems are considered, where the problems of mean square stability, stochastic l₂‐gain and state‐feedback control design are treated and solved. Solutions are obtained for both nominal and polytopic‐type uncertain systems. In all these problems, the switching obeys a dwell time constraint. In our solution, to each subsystem of the switched system, a Lyapunov function is assigned that is nonincreasing at the switching instants. The latter function is allowed to vary piecewise linearly, starting at the end of the previous switch instant, and it becomes time invariant after the dwell. In order to guarantee asymptotic stability, we require the Lyapunov function to be negative between consecutive switchings. We thus obtain Linear Matrix Inequalities conditions. Based on the solution of the stochastic l₂‐gain problem, we derive a solution to the state‐feedback control design, where we treat a variety of special cases. Being affine in the system matrices, all the aforementioned solutions are extended to the uncertain polytopic case. The proposed theory is demonstrated by a practical example taken from the field of flight control. Copyright © 2015 John Wiley & Sons, Ltd.     

Nonstationary H∞ dynamic output feedback control for discrete‐time Markov jump linear systems with actuator and sensor saturations

This paper is concerned with the nonstationary dynamic output feedback control problem for a class of discrete‐time Markov jump linear systems (MJLSs) under simultaneous consideration of actuator and sensor saturations. The so‐called nonstationary controllers dominated by two other different piecewise‐stationary Markov chains are introduced, making the designed controllers not only mode‐dependent but also dependent on other variations associated with the mode transitions in the original MJLSs. The sufficient conditions formulated in terms of bilinear matrix inequalities for the H_∞ control problem are established such that the resulting closed‐loop system is stochastically stable and achieves a prescribed H_∞ noise attenuation level. A suboptimal algorithm with line search is exploited to solve for the associated controller gains. Effectiveness of the developed theoretical results is verified via a numerical example. Copyright © 2015 John Wiley & Sons, Ltd.     

Asynchronous fault detection observer design for discrete‐time piecewise linear systems

This paper studies the problem of asynchronous fault detection (FD) observer design for piecewise linear systems. Considering that the states of the FD observer and the system may stay at different regions of the state space, asynchronous FD observers are designed at different instants to cope with the challenges incurred by exogenous disturbances and fault signals. By employing new piecewise Lyapunov functions that depend on the different regions where the states are located, it is proved that the proposed asynchronous FD observers ensure the stability and H_∞ performance of the error systems. Three examples are given to show that the new design scheme provides better FD results than the existing design methods.     

A robust discrete‐time adaptive control approach for systems with almost periodic time‐varying parameters

A periodic adaptive control approach is proposed for a class of nonlinear discrete‐time systems with time‐varying parametric uncertainties which are almost periodic, and the only prior knowledge is the periodicity. The new adaptive controller updates the parameters and the control signal periodically in a pointwise manner over one entire period, in the sequel that achieves a bounded tracking convergence. The result is further extended to scenarios with unknown input gain, higher order dynamics, and tracking. Copyright © 2012 John Wiley & Sons, Ltd.     

Quadratic stabilizability and H∞ control of linear discrete‐time stochastic uncertain systems

This paper considers quadratic stabilizability and H_∞ feedback control for stochastic discrete‐time uncertain systems with state‐ and control‐dependent noise. Specifically, the uncertain parameters considered are norm‐bounded and external disturbance is an l²‐square summable stochastic process. Firstly, both quadratic stability and quadratic stabilization criteria are presented in the form of linear matrix inequalities (LMIs). Then we design the robust H_∞ state and output feedback H_∞ controllers such that the system with admissible uncertainties is not only quadratically internally stable but also robust H_∞ controllable. Sufficient conditions for the existence of the desired robust H_∞ controllers are obtained via LMIs. Finally, some examples are supplied to illustrate the effectiveness of our results.     

Infinite horizon linear quadratic optimal control for discrete‐time stochastic systems

This paper is concerned with the infinite horizon linear quadratic optimal control for discrete‐time stochastic systems with both state and control‐dependent noise. Under assumptions of stabilization and exact observability, it is shown that the optimal control law and optimal value exist, and the properties of the associated discrete generalized algebraic Riccati equation (GARE) are also discussed. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust Kalman filtering for uncertain discrete‐time linear systems

This paper presents a steady‐state robust state estimator for a class of uncertain discrete‐time linear systems with norm‐bounded uncertainty. It is shown that if the system satisfies some particular structural conditions and if the uncertainty has a specific structure, the gain of the robust estimator (which assures a guaranteed cost) can be calculated using a formula only involving the original system matrices. Among the conditions the system has to satisfy, the strongest one relies on a minimum phase argument. It is also shown that under the assumptions considered, the robust estimator is in fact the Kalman filter for the nominal system. Copyright © 2003 John Wiley & Sons, Ltd.     

Adaptive event‐triggered control for nonlinear discrete‐time systems

This paper focuses on the analysis and the design of event‐triggering scheme for discrete‐time systems. Both static event‐triggering scheme (SETS) and adaptive event‐triggering scheme (AETS) are presented for discrete‐time nonlinear and linear systems. What makes AETS different from SETS is that an auxiliary dynamic variable satisfying a certain difference equation is incorporated into the event‐triggering condition. The sufficient conditions of asymptotic stability of the closed‐loop event‐triggered control systems under both two triggering schemes are given. Especially, for the linear systems case, the minimum time between two consecutive control updates is discussed. Also, the quantitative relation among the system parameters, the preselected triggering parameters in AETS, and a quadratic performance index are established. Finally, the effectiveness and respective advantage of the proposed event‐triggering schemes are illustrated on a practical example. Copyright © 2016 John Wiley & Sons, Ltd.     

Decentralized adaptive consensus control for discrete‐time heterogeneous semiparametric multiagent systems

Different from the consensus control of traditional multiagent systems, this paper studies the decentralized adaptive consensus control for discrete‐time heterogeneous hidden leader‐following semiparametric multiagent system, in which the dynamic equation of each agent has both parametric uncertainties and nonparametric uncertainties. In the considered system, there is a hidden leader agent who can receive the reference signal, but it can only affect the states of those agents who are in its neighborhood. For other following agents, they do not know the leader's existence or the reference signal, and they can only receive information from their neighbors. Our goal is to design decentralized adaptive controllers to make sure that all agents can track the reference signal, and the closed‐loop system achieves consensus in the presence of mutual coupling relations. Due to the existence of both parametric and nonparametric uncertainties in the system, we need to estimate them separately. For the parametric part, we propose a novel dead zone with threshold converging to zero to modify the traditional gradient update law, while for the nonparametric part, we introduce an auxiliary variable including both two uncertainties to facilitate the nonparametric uncertainties compensation. Based on the certainty equivalence principle in adaptive control theory, the decentralized adaptive controller is designed for each agent to make sure that all of them can track the reference signal. Finally, under the proposed control protocol, strict mathematical proofs are given by using Lyapunov theory; then, simulation results are provided to demonstrate the effectiveness of proposed decentralized adaptive controllers.     

离散时间部分状态反馈模型参考自适应控制

本文针对线性不确定性系统, 给出了部分状态反馈直接模型参考自适应控制设计方案以及详细的系统稳 定性、输出跟踪性能分析. 控制器设计基于降维观测器和参数化方法. 此方案采用反馈控制, 反馈信号不仅仅依赖 全状态信息或者输出信号, 而是任意不超过系统维数的可测信号. 因此, 部分状态反馈控制是包含状态反馈、输出 反馈控制的新的控制方案, 缓解了状态反馈对状态信息的限制, 降低了输出反馈控制结构的复杂性. 通过引入辅助 信号, 本文证明了输出匹配条件的存在性、所有闭环系统信号的有界性以及渐近输出跟踪性能. 仿真结果验证了该 方案的有效性.     

Filtering of discrete‐time Markov jump linear systems with uncertain transition probabilities

This article addresses the filtering design problem for discrete‐time Markov jump linear systems (MJLS) under the assumption that the transition probabilities are not completely known. We present the methods to determine ??₂‐ and ??_∞‐norm bounded filters for MJLS whose transition probability matrices have uncertainties in a convex polytope and establish an equivalence with the ones with partly unknown elements. The proposed design, based on linear matrix inequalities, allows different assumptions on Markov mode availability to the filter and on system parameter uncertainties to be taken into account. Under mode‐dependent assumption and internal model knowledge, observer‐based filters can be obtained and it is shown theoretically that our method outperforms some available ones in the literature to date. Numerical examples illustrate this claim. Copyright © 2010 John Wiley & Sons, Ltd.     

Observer‐based controller design of discrete‐time piecewise affine systems

This paper presents a novel observer‐based controller design method for discrete‐time piecewise affine (PWA) systems. The basic idea is as follows: at first, a piecewise linear (without affine terms) state feedback controller and a PWA observer are designed separately, and then it is proved that the output feedback controller constructed by the resulting observer and state feedback controller gains can guarantee the stability of the closed‐loop system. During the controller design, the piecewise‐quadratic Lyapunov function technique is used. Moreover, the region information is taken into account to treat the affine terms, so the controller gains can be obtained by solving a set of linear matrix inequalities, which are numerically feasible with commercially available software. Three simulation examples are given finally to verify the proposed theoretical results. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Gain scheduled control for discrete‐time systems depending on bounded rate parameters

In this paper we consider a linear, discrete‐time system depending multi‐affinely on uncertain, real time‐varying parameters. A new sufficient condition for the stability of this class of systems, in terms of a feasibility problem involving linear matrix inequalities (LMIs), is obtained under the hypothesis that a bound on the rate of variation of the parameters is known. This condition, obtained by the aid of parameter dependent Lyapunov functions, obviously turns out to be less restrictive than that one obtained via the classical quadratic stability (QS) approach, which guarantees stability in presence of arbitrary time‐varying parameters. An important point is that the methodology proposed in this paper may result in being less conservative than the classical QS approach even in the absence of an explicit bound on the parameters rate of variation. Concerning the synthesis context, the design of a gain scheduled compensator based on the above approach is also proposed. It is shown that, if a suitable LMI problem is feasible, the solution of such problem allows to design an output feedback gain scheduled dynamic compensator in a controller‐observer form stabilizing the class of systems which is dealt with. The stability conditions are then extended to take into account L₂ performance requirements. Some numerical examples are carried out to show the effectiveness and to investigate the computational burden required by the proposed approach. Copyright © 2005 John Wiley & Sons, Ltd.     

Pseudo‐predictor feedback control of discrete‐time linear systems with a single input delay

This paper studies the problems of stabilization of discrete‐time linear systems with a single input delay. By developing the methodology of pseudo‐predictor feedback, which uses the (artificial) closed‐loop system dynamics to predict the future state, memoryless state feedback control laws are constructed to solve the problem. Necessary and sufficient conditions are obtained to guarantee the stability of the closed‐loop system in terms of the stability of a class‐difference equations. It is also shown that the proposed controller achieves semi‐global stabilization of the system if its actuator is subject to either magnitude saturation or energy constraints under the condition that the open‐loop system is only polynomially unstable. Numerical examples have been worked out to illustrate the effectiveness of the proposed approaches. Copyright © 2015 John Wiley & Sons, Ltd.     

Cooperative robust output regulation problem for discrete‐time linear time‐delay multi‐agent systems

In this paper, we study the cooperative robust output regulation problem for discrete‐time linear multi‐agent systems with both communication and input delays by a distributed internal model approach. We first introduce the distributed internal model for discrete‐time multi‐agent systems with both communication and input delays. Then, we define the so‐called auxiliary system and auxiliary augmented system. Finally, we solve our problem by showing, under some standard assumptions, that if a distributed state feedback control or a distributed output feedback control solves the robust output regulation problem of the auxiliary system, then the same control law solves the cooperative robust output regulation problem of the original multi‐agent systems.     

一类组合系统的模型参考自适应分散控制

针对一类组合系统的模型参考自适应分散控制问题,提出一种新的考虑问题的思路.在选择参考模型时,根据系统所期望的性能指标,考虑各子系统间的相互作用,保留互联项;基于Lyapunov稳定性理论,给出了模型参考自适应控制方案,并证明了其整体一致收敛性.