Markov跳变系统的有限时间状态反馈镇定

讨论一类含有限能量未知扰动的线性Markov跳变系统的有限时间镇定问题.针对连续系统和离散系统两种情况,利用构造的Lyapunnov-Krasovskii函数,并结合线性矩阵不等式方法,分别证明并给出了跳变系统有限时间镇定控制器有解的充分条件.采用该方法设计的镇定控制器可使连续系统和离散系统对所有满足条件的未知扰动是有限时间有界和有限时间镇定的.最后通过数值示例表明了该设计方法的有效性.

     

时滞执行器饱和Markov跳变系统的有限时间镇定

讨论了含执行器饱和的离散时滞Markov跳变系统在未知但有界扰动的情况下,针对系统模态转移概率部分未知的系统进行有限时间镇定的分析和研究。利用构造的Lyapunov函数和饱和非线性处理技术,对具有执行器饱和的离散时滞Markov系统进行研究,并提出了系统状态有限时间镇定的充分条件,结合线性矩阵不等式的方法,设计并实现了有限时间镇定状态反馈控制器。通过数值仿真,示例验证了该设计方法的有效性及潜在的应用性。     

随机系统输出概率密度函数的有限时间镇定

针对一类含有限能量未知扰动的随机动态系统,研究基于随机分布函数的有限时间控制问题.通过B样条逼近建立了输出概率密度函数(PDF)与权值之间的对应关系,利用线性矩阵不等式,给出了基于观测器的PDF有限时间控制器的参数化设计方法.采用该方法设计的控制器,可使系统对所有满足条件的未知扰动是随机有限时间有界和随机有限时间镇定的.仿真实例验证了所提出方法的有效性.     

随机系统输出概率密度函数的有限时间镇定

针对一类含有限能量未知扰动的随机动态系统,研究基于随机分布函数的有限时间控制问题．通过Ｂ 样条逼近建立了输出概率密度函数（ＰＤＦ）与权值之间的对应关系,利用线性矩阵不等式,给出了基于观测器的ＰＤＦ 有限时间控制器的参数化设计方法．采用该方法设计的控制器,可使系统对所有满足条件的未知扰动是随机有限时间有界和随机有限时间镇定的．仿真实例验证了所提出方法的有效性．

     

T-S模糊系统的有限时间控制

面向具有强非线性的复杂工业过程,利用T-S模糊模型逼近原非线性系统,把T-S模糊模型逼近非线性系统存在的误差描述成有界时变的扰动,进而提出带扰动的T-S模糊系统的有限时间控制方法.首先,给出线性系统有限时间有界性的一个充分条件,与现有结果相比,该条件具有较小的保守性,并可以处理扰动是时变的情况;然后,提出T-S模糊系统有限时间镇定控制器的设计方法;最后,给出基于线性矩阵不等式(LMI)的控制器设计算法,并通过数值算倒演示所给方法的有效性.     

基于输出反馈和滑模控制的一类二阶非线性系统有限时间镇定方法

本文研究了一类具有不确定非线性动力学和未知外部扰动的二阶非线性系统的全局有限时间输出镇定问 题. 首先, 提出了一种全局状态反馈有限时间控制器, 实现了二阶非线性系统的有限时间镇定. 为了解决只有系统输 出可用这种更有挑战性的情况, 采用了一种新颖的设计思想, 即非分离原理. 构造了一个有限时间收敛的状态观测 器来估计未知状态. 在此观测器的基础上, 提出了一种基于输出的有限时间复合控制器. 基于李雅普诺夫方法, 证明 了整个闭环系统的全局有限时间稳定性. 仿真结果表明了理论的有效性.     

随机马尔科夫跳跃系统有限时间控制

研究了转移概率部分信息未知的随机马尔科夫跳跃系统的有限时间控制问题.首先,介绍了有限时间随机稳定性与随机镇定性的概念;然后,利用矩阵变换、数学期望以及Gronwall不等式等方法,给出了系统为有限时间随机稳定的判定准则.利用上述结果,得出了系统状态输出反馈随机镇定的充分条件;进一步,考虑到实际工程中系统状态的不完全可测性,给出了保证系统有限时间随机镇定的动态输出反馈控制器设计方式,并求得了此控制器存在的判定条件.最后,用一个数值算例说明了控制器设计方法的有效性.     

基于扩展状态观测器的随机隐Markov正跳变系统有限时间异步控制

针对一类含不匹配扰动的随机隐Markov跳变系统, 本文研究了基于扩展状态观测器(ESO)的有限时间异步 控制问题. 首先, 引入一组扩展变量将隐Markov跳变系统转换成一组新的随机扩展系统, 补偿不匹配扰动对系统控 制输出的影响. 基于Lyapunov–Krasovskii泛函方法, 给出使得基于ESO的闭环随机隐Markov增广跳变系统是正系 统, 且有限时间有界的充分条件. 进而得到直接求解观测器增益和控制器增益的线性矩阵不等式. 最后, 通过仿真结 果验证了本文所设计的异步状态反馈控制器和观测器的有效性和可行性.     

一类二阶非线性系统的有限时间状态反馈镇定方法

针对一类二阶非线性系统的有限时间状态反馈镇定问题进行了讨论. 给出了三种基于连续状态反馈的全局有限时间状态反馈镇定方法. 首先，利用非线性齐次系统性质，设计出一种状态反馈控制器，使得闭环系统渐近稳定并且具有负的齐次度；其次，基于有限时间Lyapunov函数的反步构造法，给出了一种有限时间控制器；最后，利用非奇异终端滑模控制技术，得到了一种使闭环系统有限时间收敛到平衡点的反馈镇定控制器. 仿真结果表明了这些方法的有效性.     

时变时滞连续切换奇异系统的一致有限时间稳定分析

讨论一类含有时变时滞的连续时间切换奇异系统的一致有限时间稳定、有限时间有界和状态反馈镇定问题. 在给定任意的切换规则下, 运用多Lyapunov 函数和平均驻留时间方法设计使得闭环系统一致有限时间稳定和有限时间有界的状态反馈控制器, 同时给出基于线性矩阵不等式表示的控制器存在的充分条件. 最后通过数值算例表明了所提出方法的合理性和有效性.

     

Observer‐based finite‐time stabilization for extended Markov jump systems

In this paper, we study the problem of observer‐based finite‐time stabilization for a class of extended Markov jump systems with norm‐bounded uncertainties and external disturbances. The stochastic character under consideration is governed by a finite‐state Markov process, but with only partial information on the transition jump rates. Based on the finite‐time stability analysis, sufficient conditions for the existence of the observer‐based controller are derived via a linear matrix inequality approach such that the closed‐loop system trajectory stays within a prescribed bound in a fixed time interval. When these conditions are satisfied, the designed observer‐based controller gain matrices can be obtained by solving a convex optimization problem. Simulation results demonstrate the effectiveness of the approaches proposed in this paper. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Finite‐time stability and stabilization of semi‐Markovian jump systems with time delay

Semi‐Markovian jump systems are more general than Markovian jump systems in modeling practical systems. On the other hand, the finite‐time stochastic stability is also more effective than stochastic stability in practical systems. This paper focuses on the finite‐time stochastic stability, exponential stochastic stability, and stabilization of semi‐Markovian jump systems with time‐varying delay. First, a new stability condition is presented to guarantee the finite‐time stochastic stability of the system by using a new Lyapunov‐Krasovskii functional combined with Wirtinger‐based integral inequality. Second, the stability criterion is further proved to guarantee the exponential stochastic stability of the system. Moreover, a controller design method is also presented according to the stability criterion. Finally, an example is provided to illustrate that the proposed stability condition is less conservative than other existing results. Additionally, we use the proposed method to design a controller for a load frequency control system to illustrate the effectiveness of the method in a practical system of the proposed method.     

Stochastic switched controller design of networked control systems with a random long delay

The problem of stabilizing Networked Control Systems (NCSs) with random but bounded delays is discussed in this paper. By using an augmented state‐space method, this class of problem can be modeled as a discrete‐time jump linear system governed by finite‐state Markov chains. As the network‐induced time vary delay of NCSs changes along with the network transferring route and the network load, results in systems becoming instable with controller designs based on a fixed transition matrix, we firstly make use of the V‐K iteration algorithm to design m groups of stabilizing controllers that satisfy different m transition matrixes, and then constitute a switched controller for them and a switch. The simulation shows that if the switched controller is used to stabilize the discrete‐time jump linear system, this system not only has a larger stabilizing span, but also has better dynamic stabilizing characters compared to those with only one group of controllers. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Finite horizon quadratic optimal control and a separation principle for Markovian jump linear systems

In this note, we consider the finite-horizon quadratic optimal control problem of discrete-time Markovian jump linear systems driven by a wide sense white noise sequence. We assume that the output variable and the jump parameters are available to the controller. It is desired to design a dynamic Markovian jump controller such that the closed-loop system minimizes the quadratic functional cost of the system over a finite horizon period of time. As in the case with no jumps, we show that an optimal controller can be obtained from two coupled Riccati difference equations, one associated to the optimal control problem when the state variable is available, and the other one associated to the optimal filtering problem. This is a principle of separation for the finite horizon quadratic optimal control problem for discrete-time Markovian jump linear systems. When there is only one mode of operation our results coincide with the traditional separation principle for the linear quadratic Gaussian control of discrete-time linear systems.     

Observer‐based finite‐time stabilization for discrete‐time switched singular systems with quadratically inner‐bounded nonlinearities

This paper discusses the observer‐based finite‐time stabilization for discrete‐time switched singular systems with quadratically inner‐bounded nonlinear terms. Firstly, based on the Luenberger‐like observer, by using the average dwell time approach, sufficient conditions are proposed to make closed‐loop systems be regular, be causal, as having a unique solution, and be uniformly finite‐time bounded. Then, a new linear matrix inequality sufficient condition for the existence of an observer‐based controller is obtained by using certain matrix decoupling techniques, and the controller is designed. In this paper, the conditions proposed not only give the observer‐based controller design methods but also guarantee the existence and uniqueness of solution for the systems. Since the quadratically inner‐bounded nonlinearities are more general than Lipschitz nonlinearities and one‐sided Lipschitz nonlinearities, compared with previous works, the proposed controller design methods in this paper are also more general than the existing ones. Finally, numerical examples are provided to illustrate the effectiveness of the methods proposed in this paper.     

Robust stability,stabilization and ℋ∞ control of time‐delay systems with Markovian jump parameters

In this paper, the problems of stochastic stability and stabilization for a class of uncertain time‐delay systems with Markovian jump parameters are investigated. The jumping parameters are modelled as a continuous‐time, discrete‐state Markov process. The parametric uncertainties are assumed to be real, time‐varying and norm‐bounded that appear in the state, input and delayed‐state matrices. The time‐delay factor is constant and unknown with a known bound. Complete results for both delay‐independent and delay‐dependent stochastic stability criteria for the nominal and uncertain time‐delay jumping systems are developed. The control objective is to design a state feedback controller such that stochastic stability and a prescribed ?_∞‐performance are guaranteed. We establish that the control problem for the time‐delay Markovian jump systems with and without uncertain parameters can be essentially solved in terms of the solutions of a finite set of coupled algebraic Riccati inequalities or linear matrix inequalities. Extension of the developed results to the case of uncertain jumping rates is also provided. Copyright © 2003 John Wiley & Sons, Ltd.     

Control of discrete‐time periodic linear systems with input saturation via multi‐step periodic invariant sets

This paper studies local control of discrete‐time periodic linear systems subject to input saturation by using the multi‐step periodic invariant set approach. A multi‐step periodic invariant set refers to a set from which all trajectories will enter a periodic invariant set after finite steps, remain there forever, and eventually converge to the origin as time approaches infinity. The problems of (robust) estimation of the domain of attraction, (robust) local stabilization (with bounded uncertainties), and disturbance rejection are considered. Compared with the conventional periodic invariant set approach, which has been used in the literature for local stability analysis and stabilization of discrete‐time periodic linear systems subject to input saturation, this new invariant set approach is capable of significantly reducing the conservatism by introducing additional auxiliary variables in the set invariance conditions. Moreover, the new approach allows to design (robust) stabilizing periodic controller, in the presence of norm bounded uncertainties, whose period is the same as the open‐loop system and is different from the existing periodic enhancement approach by which the period of the controller is multiple times of the period of the open‐loop system. Several numerical examples are worked out to show the effectiveness of the proposed approach. Copyright © 2013 John Wiley & Sons, Ltd.     

Stabilization of Markov jump linear systems using quantized state feedback

This paper addresses the stabilization problem for single-input Markov jump linear systems via mode-dependent quantized state feedback. Given a measure of quantization coarseness, a mode-dependent logarithmic quantizer and a mode-dependent linear state feedback law can achieve optimal coarseness for mean square quadratic stabilization of a Markov jump linear system, similar to existing results for linear time-invariant systems. The sector bound approach is shown to be non-conservative in investigating the corresponding quantized state feedback problem, and then a method of optimal quantizer/controller design in terms of linear matrix inequalities is presented. Moreover, when the mode process is not observed by the controller and quantizer, a mode estimation algorithm obtained by maximizing a certain probability criterion is given. Finally, an application to networked control systems further demonstrates the usefulness of the results.