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.     

Robust extended dissipative control for sampled-data Markov jump systems

This paper investigates the problem of the sampled-data extended dissipative control for uncertain Markov jump systems. The systems considered are transformed into Markov jump systems with polytopic uncertainties and sawtooth delays by using an input delay approach. The focus is on the design of a mode-independent sampled-data controller such that the resulting closed-loop system is mean-square exponentially stable with a given decay rate and extended dissipative. A novel exponential stability criterion and an extended dissipativty condition are established by proposing a new integral inequality. The reduced conservatism of the criteria is demonstrated by two numerical examples. Furthermore, a sufficient condition for the existence of a desired mode-independent sampled-data controller is obtained by solving a convex optimisation problem. Finally, a resistance, inductance and capacitance (RLC) series circuit is employed to illustrate the effectiveness of the proposed approach.     

Markov跳变系统的非同步事件触发耗散容错控制

本文主要研究一类具有执行器故障的Markov跳变系统的非同步事件触发耗散容错控制问题.通过引入非同步事件触发器来降低传感器的采样数据传输频率,从而降低通信消耗.采用两个独立的隐Markov模型分别描述触发器、控制器与原系统之间的非同步现象.在此框架下,基于Lyapunov稳定性和耗散理论,得到了闭环控制系统在执行器存在故障的情况下随机稳定并严格耗散的充分条件.并借助矩阵不等式变换技术给出了触发器和控制器矩阵参数的求解方法,实现了触发器和控制器的协同设计.最后,通过仿真研究验证了所提出的设计方法的有效性.     

基于扩张状态观测器的分散模型预测控制

针对复杂关联系统中分散控制方法无法有效解决子系统间的耦合和干扰问题, 提出一种基于扩张状态观测器的分散模型预测控制算法. 首先将复杂关联系统分解为多个状态维数较低、控制变量较少的子系统, 并为每个子系统设计本地预测控制器; 然后, 采用扩张状态观测器对子系统的耦合项以及干扰项进行估计, 进而利用估计值对子系统进行前馈补偿, 从而降低复杂关联系统的计算复杂度, 提高系统的稳定性和抗干扰能力; 最后, 利用液位控制系统验证了所提出算法的有效性.

     

Derandomisation-based multiple frequency control for stochastic Markov jump systems

Under the framework of derandomisation approach, the state feedback control issues for both continuous-time and discrete-time Markov jump linear systems (MJLSs) are investigated to meet multiple performance objectives over multiple frequency ranges. Because of the stochastic jumping among different modes, the generalised Kalman–Yakubovic–Popov lemma-based finite-frequency controller design approach cannot be directly applied to MJLSs. To overcome this limitation, a derandomisation approach is established by transforming the original stochastic multiple modes systems to deterministic ones. Then the multiple frequency controllers for both discrete-time and continuous-time MJLSs are designed to guarantee the multiple performances of the closed-loop systems. To verify the effectiveness of the developed algorithms, examples are presented, where the performance requirements include specifications in low-frequency and high-frequency ranges, respectively.     

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Lyapunov-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问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.     

Hidden Markov model based filtering for singular semi-Markov jump systems

This article investigates the hidden Markov model based filter design problem for the singular semi-Markov jump systems (SSMJSs). The considered semi-Markov process is a generalization of Markov process, which can eliminate the restriction on the exponential distribution of sojourn time. Besides, the hidden Markov model based filter is introduced to tackle the asynchronous phenomenons occurred between the system modes and filter modes. To ensure the stochastic stability of the SSMJSs and derive solvable filter parameters, a filter design technic is constructed. First, the direct evolution of the states between two arbitrary close time instants is constructed from the filtering error system according to slow-fast decomposition, sufficient conditions are then proposed based on the consistent projector of the filtering error system and the constructed direct state evolution. Second, a new linear decoupling strategy is presented to deal with the coupled terms under the established stability conditions, which further derives the desired hidden Markov model based filter parameters. A numerical example is given to illustrate the effectiveness of the proposed method.     

随机时滞马尔可夫跳跃系统的比例-积分跟踪控制

针对具有时变时滞和未知非线性的随机马尔可夫跳变系统,基于传统的PI控制策略和线性矩阵不等式算法,提出一种具有随机稳定性能、跟踪性能和鲁棒性能的多目标控制器设计方案.运用Lyapunov稳定性理论并引入L<,1>性能指标,构造出具有PI结构的跟踪控制器,保证了随机马尔可大跳跃系统的稳定性和跟踪性能,实现了系统跟踪性能的优...     

A novel suboptimal algorithm for state estimation of Markov jump linear systems

This paper is concerned with state estimation problem for Markov jump linear systems where the disturbances involved in the systems equations and measurement equations are assumed to be Gaussian noise sequences.Based on two properties of conditional expectation,orthogonal projective theorem is applied to the state estimation problem of the considered systems so that a novel suboptimal algorithm is obtained.The novelty of the algorithm lies in using orthogonal projective theorem instead of Kalman filters to estimate the state.A numerical comparison of the algorithm with the interacting multiple model algorithm is given to illustrate the effectiveness of the proposed algorithm.     

Markov跳变系统的输出反馈鲁棒预测控制

对离散时间Markov跳变系统, 当系统状态不完全可测时, 研究了一类基于输出反馈的鲁棒模型预测控制问题. 所研究系统为准线性参数时变的, 考虑在当前时刻系统的时变参数是已知的, 将来时刻未知的情况. 综合考虑系统存在多胞不确定性和有界噪声等因素, 通过运用线性矩阵不等式方法及变量变换思想, 将无穷时域性能指标的最小最大鲁棒预测控制问题转化为具有线性矩阵不等式约束的凸优化问题, 得到了系统的输出反馈控制律. 引入二次有界概念, 在满足输入输出约束的情况下, 保证闭环系统的随机稳定性. 数值算例验证了方法的有效性.     

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.     

Static output feedback control for discrete‐time hidden Markov jump systems against deception attacks

This paper investigates the static output feedback control problem for Markov jump systems subject to asynchronous mode information and deception attacks. A hidden Markov model is employed to observe the unmeasurable system mode. In this case, the asynchronous phenomenon between the controller and the original system is depicted. By using the mode‐dependent Lyapunov function, a sufficient condition is established such that the resulting closed‐loop system is stochastically mean square exponentially ultimately bounded under randomly occurring deception attacks and external disturbance. Based on this condition, the asynchronous static output feedback controller is designed in view of linear matrix inequalities. Finally, the effectiveness and superiority of the presented method are elaborated via a numerical example and a practical example.     

基于扩张状态观测器的永磁同步电机重复学习控制

本文针对非参数不确定永磁同步电机系统,提出一种基于扩张状态观测器的重复学习控制方法,实现对周期期望轨迹的高精度跟踪.首先,将永磁同步电机中的非参数不确定性分为周期不确定与非周期不确定两部分.其次,构造包含周期不确定的未知期望控制输入,并设计重复学习律估计未知期望控制输入并补偿系统周期不确定.在此基础上,设计扩张状态观测器,估计系统未知状态和补偿非周期性不确定,进而提高系统鲁棒性.与已有的部分限幅学习律相比,本文提出的全限幅重复学习律可以保证估计值的连续性且能够被限制在指定的界内.最后,基于李雅普诺夫方法分析误差的收敛性能,并给出仿真和实验结果验证本文所提方法的有效性.     

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     

An LP approach to full-order and reduced-order state estimations of positive Markov jump systems with delay

In this paper, the problems of full-order and reduced-order positive state estimations are developed for discrete-time positive Markov jump linear systems with delay. By establishing a positive time-delay system for 1-moment function of the state vector, delay-dependent necessary and sufficient exponential stability conditions are first derived based on a comparison technique for positive systems. Then, on the basis of the derived stability conditions, the problems of designing positive state observers in full-order and reduced-order for positive Markov jump systems with delay are addressed. The existence conditions of positive observers and the design schemes are formulated in terms of linear programming problems which can be effectively solved by various optimisation algorithms to obtain the observer parameters. Finally, three numerical examples with simulations are given to validate the analysis and design results.     

Hybrid-triggered scheme asynchronous control for hidden Markov jump systems with partially unknown probabilities and cyber attacks

This paper is concerned with the issue of hybrid-triggered scheme $H_{\infty }$ asynchronous control for networked Markov jump systems (MJSs) with probabilistic cyber attacks. First, in view of the subsistent phenomenon that the controller cannot capture the system modes synchronously, the hidden Markov model (HMM) with partly unknown probabilities is introduced in this article to describe such asynchronous phenomenon. In addition, the hybrid-triggered scheme includes time-triggered scheme and event-triggered scheme, in which the switching signal between two schemes obeys random Bernoulli distribution. By utilizing Lyapunov stability theory and matrix inequality technique, some sufficient conditions are developed, which can guarantee the networked MJSs mean-square asymptotically stable (MSAS) and $H_{\infty }$ performance; also, the desired controller gains are obtained by singular value decomposition (SVD) methods. Moreover, as the special cases of the results above, three corollaries are given. Finally, a numerical example and a pulse width-modulation-driven boost converter (PWMDBC) model are provided to demonstrate the usefulness and reliability of our developed approaches.     

随机马尔可夫跳变系统的变结构控制设计

采用滑动扇区方法,研究了不确定随机马尔可夫跳变系统的变结构控制设计问题。首先给出随机马尔可夫跳变系统滑动扇区的定义,然后基于线性矩阵不等式技术,提出一种滑动扇区及变结构控制律设计方法。经过理论证明该控制律能够确保随机马尔可夫跳变不确定系统二次稳定,并有效地抑制抖振。最后数值仿真算例验证了控制方案的有效性。     

Stochastic stability analysis of integral non-homogeneous Markov jump systems

This paper investigates the problem of stability analysis for time-delay integral Markov jump systems with time-varying transition rates. Some free-weight matrices are addressed and sufficient conditions are established under which the system is stochastically stable. The bound of delay is larger than those in other results obtained, which guarantees that the proposed conditions are tighter. Numerical examples show the effectiveness of the method proposed.