Reliable dissipative control for stochastic impulsive systems

This paper deals with the problem of reliable dissipative control for a class of stochastic hybrid systems. The systems under study are subject to Markovian jump, parameter uncertainties, possible actuator failure and impulsive effects, which are often encountered in practice and the sources of instability. Our attention is focused on the design of linear state feedback controllers and impulsive controllers such that, for all admissible uncertainties as well as actuator failure occurring among a prespecified subset of actuators, the stochastic hybrid system is stochastically robustly stable and strictly (Q,S,R)-dissipative. The sufficient conditions are obtained by using linear matrix inequality (LMI) techniques. The main results of this paper extend the existing results on H^∞ control.     

Robust normalization and guaranteed cost control for a class of uncertain singular Markovian jump systems via hybrid impulsive control

This paper investigates the problem of robust normalization and guaranteed cost control for a class of uncertain singular Markovian jump systems. The uncertainties exhibit in both system matrices and transition rate matrix of the Markovian chain. A new impulsive and proportional‐derivative control strategy is presented, where the derivative gain is to make the closed‐loop system of the singular plant to be a normal one, and the impulsive control part is to make the value of the Lyapunov function does not increase at each time instant of the Markovian switching. A linearization approach via congruence transformations is proposed to solve the controller design problem. The cost function is minimized via solving an optimization problem under the designed control scheme. Finally, three examples (two numerical examples and an RC pulse divider circuit example) are provided to illustrate the effectiveness and applicability of the proposed methods. Copyright © 2013 John Wiley & Sons, Ltd.     

Reliable dissipative control for uncertain time‐delayed stochastic systems with Markovian jump switching and multiplicative noise

This paper considers the robust reliable dissipative control problem for a class of hybrid systems, which includes stochastics, Markovian jumping, state time delay, parameter uncertainty, possible actuator failure, multiplicative noises and impulsive effects. We propose a linear feedback memoryless controller and impulsive controller such that the hybrid system is stochastically stable and strictly (Q, S, R) dissipative, which include H_∞ performance as a special case, for all the admissible uncertainties and actuator failures occurring among a prescribed subset of actuators. Based on Itô's differential formula and Lyapunov stability theory, sufficient conditions are obtained in terms of linear matrix inequalities. A numerical example is constructed to show the effectiveness of the controller designed in this paper. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Observer-based dissipative control for Markovian jump systems via delta operators

This paper addresses the issue of observer-based dissipative control problem for a class of Markovian jump systems with random delay via delta operator approach. First, based on the construction of a novel Lyapunov functional together with the use of free-weighting matrix approach, a new set of sufficient conditions is established which ensures the stochastic asymptotic stability and dissipativity of the closed-loop augmented Markovian jump delta operator system. Next, the result is extended to design an observer-based state feedback dissipative control law such that the resulting closed-loop system is stochastically asymptotically stable with the desired dissipative performance index. Further, the existence of control laws is formulated in the form of linear matrix inequalities (LMIs) which can be easily solved by using some standard numerical packages. Also, the observer and control gains can be calculated by using the solutions of an obtained set of LMIs. It is worth pointing out that the dissipative control problem considered here includes the H_∞ and passivity-based control problems as special cases. Finally, two numerical examples with simulation are presented to demonstrate the effectiveness of the obtained design technique.     

广义线性系统的分散控制

从混合型输出反馈控制的角度讨论了广义线性系统的分散控制问题，给出了一个广义性系统在混合型分散输出反馈下存在脉冲固定模的充分条件，提出卫通过实现分散正常化消除脉冲固定模的有效算法。     

p-Moment stability of stochastic differential equations with impulsive jump and Markovian switching

This paper introduces some new concepts of p-moment stability for stochastic differential equations with impulsive jump and Markovian switching. Some stability criteria of p-moment stability for stochastic differential equations with impulsive jump and Markovian switching are obtained by using Liapunov function method. An example is also discussed to illustrate the efficiency of the obtained results.     

线性时滞系统的耗散控制

研究了一类线性时滞系统的二次耗散控制问题,基于线性矩阵不等式（LMI）方法导出了耗散控制器存在的充分条件,通过线性矩阵不等式的可行解构造出耗散态状态反馈和动态输出反馈控制律,相应的闭环系统是二次稳定和严格（Q,S,R）耗散的,本文的主要贡献是统一了线性时滞系统现有的H∞控制和无源控制结果。     

Fundamental Issues in Networked Control Systems

This paper provides a survey on modeling and theories of networked control systems (NCS). In the first part, modeling of the different types of imperfections that affect NCS is discussed. These imperfections are quantization errors, packet dropouts, variable sampling/transmission intervals, variable transmission delays, and communication constraints. Then follows in the second part a presentation of several theories that have been applied for controlling networked systems. These theories include: input delay system approach, Markovian system approach, switched system approach, stochastic system approach, impulsive system approach, and predictive control approach. In the last part, some advanced issues in NCS including decentralized and distributed NCS, cloud control system, and co-design of NCS are reviewed.      

Feedback stabilization of dissipative impulsive dynamical systems

In this paper, we derive conditions under which a dissipative impulsive dynamical system is asymptotically stabilizable by a feedback controller. Specializing the obtained results to the case of dissipative linear impulsive dynamical systems with the quadratic supply rate, we establish the corresponding sufficient conditions. Finally, simulation results are given to demonstrate the effectiveness of our results.     

On hybrid control of a class of stochastic non-linear Markovian switching systems

In this paper, we address the problem of hybrid control for a class of stochastic non-linear Markovian switching systems. First, a hybrid controller is introduced for the systems. Then under some appropriate assumptions, the stabilization condition for the systems under pure impulsive control is given. Further under impulsive control, the output feedback stabilization problem of the systems is discussed and linear output feedback controllers are designed. Finally a numerical example is provided to illustrate the effectiveness of the proposed methods.     

Passivity-based non-fragile control for Markovian jump delayed systems via stochastic sampling

This paper studies the problem of non-fragile passive control for Markovian jump delayed systems via stochastic sampling. The Markovian jumping parameters, appearing in the connection weight matrices and in two additive time-varying delay components, are considered to be different. The controller is assumed to have either additive or multiplicative norm-bounded uncertainties. The sampled-data with stochastic sampling is used to design the controller by a discontinuous Lyapunov functional. This functional fully utilises the sawtooth structure characteristics of the sampling input delay. By using the matrix decomposition method and some newly inequalities, sufficient conditions are obtained to guarantee that for all admissible uncertainties the system is robustly stochastically passive. Illustrative examples are provided to show the effectiveness of the results.     

混沌系统脉冲控制及其Matlab仿真

研究Lü混沌系统的脉冲鲁棒镇定问题,得到其脉冲鲁棒镇定的充分条件,给出相应的脉冲控制律.通过应用Matlab中Simulink工具箱对Lü混沌系统进行仿真分析,说明脉冲控制是有效的镇定受扰动混沌系统的方法.     

A Problem of Control of Markovian Processes on a Graph

The paper deals with the control of Markovian processes on a graph, provided that the control can be transferred from one node to another (neighboring) node at any time. The sufficient conditions of existence of optimal stationary nonrandomized Markovian strategies are obtained.     

线性多变量系统的鲁棒耗散控制

Robust quadratic dissipative control for a class of linear multi-variable systems with parameter uncertainties is considered, where the uncertainties are expressed in a linear fractional form. For the nominal system without uncertainties, the equivalence between quadratic dissipativeness and positive realness is established, and conditions are derived for linear systems to be quadratic dissipative. As for uncertain systems, it is shown that the robust quadratic dissipative control problem for the uncertain system can be reduced to the corresponding problem for a related system without uncertainties. The control problem concerned can be solved using LMI approach. The results of the paper unify existing results on H1 control and positive real control and provide a more flexible and less conservative control design method.     

具有马氏跳跃参数的切削加工系统控制问题研究

以单刀具垂直切削加工系统为研究对象, 引入了变进给量控制方法, 建立了具有Markov跳跃参数的时变时滞跳跃系统模型. 通过对系统的随机稳定性分析, 给出了使系统呈均方意义下指数稳定的充分条件, 同时研究了在系统参数矩阵和状态转移率非精确可知情形下的鲁棒稳定性条件, 并讨论了时变时滞参数对系统状态变量指数衰减速率的影响关系. 最后以仿真算例说明了本文所提方案的有效性.     

Control of Markovian jump discrete-time systems with norm boundeduncertainty and unknown delay

This paper studies the problem of control for discrete time delay linear systems with Markovian jump parameters. The system under consideration is subjected to both time-varying norm-bounded parameter uncertainty and unknown time delay in the state, and Markovian jump parameters in all system matrices. We address the problem of robust state feedback control in which both robust stochastic stability and a prescribed H_∞ performance are required to be achieved irrespective of the uncertainty and time delay. It is shown that the above problem can be solved if a set of coupled linear matrix inequalities has a solution     

广义分散前馈控制系统固定模的进一步研究

运用把广义分散前馈控制系统转化为不带前馈的广义分散控制系统的方法,讨论了广义 分散前馈控制系统的固定模问题,给出了若干以系统原始矩阵为基础的有穷固定模和脉冲固 定模的新判据,得到了一些有意义的结论.     

Consensus of multi-agent linear dynamic systems via impulsive control protocols

In this article, we introduce impulsive control protocols for multi-agent linear dynamic systems. First, an impulsive control protocol is designed for network with fixed topology based on the local information of agents. Then sufficient conditions are given to guarantee the consensus of the multi-agent linear dynamic systems by the theory of impulsive systems. Furthermore, how to select the discrete instants and impulsive matrices is discussed. The case that the topologies of networks are switching is also considered. Numerical simulations show the effectiveness of our theoretical results.     

Distributed Model Predictive Control with Actuator Saturation for Markovian Jump Linear System

This paper is concerned with the distributed model predictive control (MPC) problem for a class of discrete-time Markovian jump linear systems (MJLSs) subject to actuator saturation and polytopic uncertainty in system matrices. The global system is decomposed into several subsystems which coordinate with each other. A set of distributed controllers is designed by solving a min-max optimization problem in terms of the solutions of linear matrix inequalities (LMIs). An iterative algorithm is developed to achieve the online computation. Finally, a simulation example is employed to show the effectiveness of the proposed algorithm.      

Consensus of Delayed Multi‐agent Systems via Intermittent Impulsive Control

A novel intermittent impulsive scheme is presented to realize consensus of multi‐agent systems with time‐varying delay in this paper because intermittent impulsive control may break through the limitation of upper bound of impulsive intervals in general impulsive control in our consensus scheme. Instead of activating all the time, we introduce the intermittent impulsive control approach into the delayed multi‐agent systems where the impulsive controller is only functioned in the control windows. Based on the algebraic graph theory, the Lyapunov stability theory, and Halanay inequality matrix theory, some adequate conditions are proposed to guarantee the consensus of delayed multi‐agent systems via pinning intermittent impulsive control. Simulation results are provided ultimately to verify the validity of the proposed control mechanism.