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.     

Stability and dissipativity analysis for uncertain Markovian jump systems with random delays via new approach

This paper studies the problem of stability and dissipativity analysis for uncertain Markovian jump systems (UMJSs) with random time-varying delays. Based on the auxiliary function-based integral inequality (AFBII) and with the help of some mathematical tools, a new double integral inequality (NDII) is developed. Then, to show the efficiency of the proposed inequality, a suitable Lyapunov-Krasovskii functional (LKF) is constructed with augmented delay-dependent terms. By employing integral inequalities, new delay-dependent sufficient conditions are derived in terms of linear matrix inequalities (LMIs). Finally, illustrative examples are given to show the effectiveness and less conservatism of the results.     

Hidden Markov model-based ℋ∞ control for singular Markov jump systems under denial of service attacks

This work investigates the control problem of discrete-time singular Markov jump systems against denial of service attacks, in which the Markov state information is seen as restricted access. To solve this situation, a hidden Markov model is introduced. The main objective is to construct a controller with the help of hidden Markov model such that the stochastically admissible of the closed-loop singular Markov jump systems with limited access mode information can be guaranteed under denial of service attacks. To produce the needed hidden Markov model-based controller, a matrix contract transformation approach is developed. At the end, a numerical example and a tunnel diode circuit are presented to demonstrate the effectiveness and benefit of the design technique described in this research.     

随机观测时滞系统的最优估计

研究了在观测中存在Markov跳跃时滞的离散时间系统的线性最小方差状态估计问题. 首先, 通过引入跳跃时滞的示性函数, 将带有跳跃时滞的观测方程转化为带有乘性噪声的定常时滞系统. 进一步采用状态扩维的方法, 将定常时滞系统转化为无时滞的Markov跳跃系统. 最后, 基于得到的无时滞系统, 采用Hilbert空间已有的几何论知识, 设计线性最优状态估计器, 得出基于Riccati方程的滤波器的表达式, 并证明了所得滤波器的渐渐收敛性.     

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.     

Observer-based sliding mode control of Markov jump systems with random sensor delays and partly unknown transition rates

In this paper, the sliding mode control problem of Markov jump systems (MJSs) with unmeasured state, partly unknown transition rates and random sensor delays is probed. In the practical engineering control, the exact information of transition rates is hard to obtain and the measurement channel is supposed to subject to random sensor delay. Design a Luenberger observer to estimate the unmeasured system state, and an integral sliding mode surface is constructed to ensure the exponential stability of MJSs. A sliding mode controller based on estimator is proposed to drive the system state onto the sliding mode surface and render the sliding mode dynamics exponentially mean-square stable with H_∞ performance index. Finally, simulation results are provided to illustrate the effectiveness of the proposed results.     

Necessary and sufficient conditions for mean square consensus under Markov switching topologies

This article deals with the mean square consensus problem for second-order discrete-time multi-agent systems. Both cases of systems with and without time delays in Markov switching topologies are considered. With the introduced control protocols, necessary and sufficient conditions for mean square consensus of second-order multi-agent systems are derived. Under the given control protocols in Markov switching topologies, the second-order multi-agent systems can reach mean square consensus if and only if each union of the graphs corresponding to all the nodes in closed sets has a spanning tree. Finally, a simulation example is provided to illustrate the effectiveness of our theoretical results.     

具有噪声约束的 时滞Markov跳变网络给定时间一致性协议设计

本文研究网络连接系统在随机Markov跳变拓扑结构,通信时滞,外部干扰等情形下的给定时间一致性协议设计方法.基于有限短时间理论,放宽对系统不一致状态渐近收敛于零的要求,在预先给定的时间区域内,设法使网络中各子系统的不一致状态在期望范围内受限运动,从而提出给定时间一致性定义,并进一步设计给定时间一致性控制算法.不仅从时间角度为降低渐近一致的工程保守性提供了思路,且所提的模型转换新方法使得设计的控制协议更具通用性.仿真结果验证了所提算法的有效性.     

基于自适应事件触发的半马尔科夫跳变系统的有限时间L2-L∞控制

本文使用马尔科夫过程的变体半马尔科夫过程建立了连续时间半马尔科夫跳变系统,并针对该系统研究了有限时间L₂–L_∞控制问题.首先,为了处理网络带宽有限的问题,在传感器通道中引入一种自适应事件触发机制,用以降低系统中的数据传输频率,从而降低通信负担.其次,考虑系统模态不可测的情况,以一定概率对其进行估计,进而研究了异步控制问题.然后,考虑了外部干扰,并引入了L₂–L_∞性能指标,研究了有限时间控制问题.本文的设计目标是在确保闭环系统有限时间稳定和满足一定性能指标的同时,降低系统中的通信负担.基于Lyapunov理论,得到状态反馈控制的设计算法.最后,用RLC电路作为实例来验证算法的有效性和可用性.     

线性Markov 切换系统的随机Nash 微分博弈及混合H2/H∞ 控制

研究线性Markov切换系统的随机Nash微分博弈问题。首先借助线性Markov切换系统随机最优控制的相关结果,得到了有限时域和无线时域Nash均衡解的存在条件等价于其相应微分(代数) Riccati方程存在解,并给出了最优解的显式形式;然后应用相应的微分博弈结果分析线性Markov切换系统的混合H2/H∞控制问题;最后通过数值算例验证了所提出方法的可行性。     

Delay-dependent H ∞ stabilisation criterion for continuous-time networked control systems with random delays

This article mainly addresses the H _∞ stabilisation problem for a class of networked control systems (NCSs) with random input delays in the continuous-time domain. A Markov jump linear system (MJLS) model with two jump parameters is developed which takes both the sensor-to-controller and controller-to-actuator delays into account. Based on such a MJLS, a new Lyapunov–Krasovskii functional is proposed to establish a delay-dependent H _∞ stabilisation criterion in terms of linear matrix inequalities (LMIs), and a mode-dependent state-feedback controller of NCSs can be determined. Two numerical examples are included to illustrate the derived result.     

线性Markov跳变随机系统的Pareto最优控制

目前针对多个主体、多个目标的带有Markov跳变的线性随机系统的控制问题的研究较少且较为浅显.本文研究了具有乘性噪声的连续时间线性Markov跳变随机系统的Pareto最优控制问题.假设多个主体、多个性能指标由状态和控制变量中的二次部分和线性部分的线性组合而形成,证明了Pareto最优与加权和优化之间的关系,从而将多目标优化问题转化为特殊的单目标加权和最优控制问题.基于Pareto博弈理论与广义It?o公式,系统的Pareto有效策略可以通过一组耦合的广义Riccati微分方程与一组耦合的线性微分方程求解,并且可以得到每一个控制器的Pareto解.最后,本文通过数值仿真验证理论结果的有效性.     

离散Markov跳变系统的滚动时域H_∞跟踪控制

针对离散Markov跳变系统,研究滚动时域H∞跟踪控制问题。为便于工程应用,假定系统当前时刻的状态和模态总是可测的,而系统未来时刻的模态是不可知的。利用庞特里亚金极小值原理,构造哈密尔顿函数,求解min-max优化问题,得到当前采样时刻的最优控制作用以及最严峻的外界扰动。控制器的求解可等效为在一组线性矩阵不等式约束条件下,迭代方程的可解性问题。控制律采用滚动时域结构,每次仅施加当前采样时刻计算得到的控制作用,在下一采样时刻将重新计算控制作用。该控制律保证系统在给定H∞扰动抑制水平的情形下,获得最优线性二次型性能指标以及良好的输出跟踪性能。最后仿真示例验证了该方法的可行性和有效性。