共查询到18条相似文献,搜索用时 61 毫秒
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本文研究一类非齐次马尔可夫跳跃正线性系统的稳定与镇定问题.该系统中模态的变化服从非齐次马尔可夫过程,其模态转移速率/概率矩阵是随时间随机变化的,且变化规律由一个高层马尔可夫过程描述,本文提出一种双层马尔可夫跳跃正系统模型来刻画此类系统特征.在此基础上,利用切换线性余正李雅普诺夫函数给出此类连续和离散时间非齐次马尔可夫跳跃正线性系统平均稳定的判据.然后,运用线性规划方法设计依赖于模态–模态转移速率/概率矩阵的状态反馈控制器,进而实现闭环系统的平均稳定性.最后,以功率分配系统为例给出仿真算例,验证了所设计控制策略的有效性. 相似文献
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研究了一类离散线性切换系统在切换时间、切换次数固定的情况下的二次最优控制问题.利用离散动态规划的方法,将多级决策过程分解成一系列易于求解的单级决策过程,求出最优控制序列和最优切换序列,并给出算法.最后通过一个数值例子来说明所提出的方法的有效性. 相似文献
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研究受L2范数有界未知扰动影响的一类马尔可夫跳跃线性系统的基于观测器的故障诊断滤波器设计问题.应用H∞优化技术,给出并证明了随机稳定并满足一定性能指标的残差产生系统的存在条件.通过求解线性矩阵不等式可求得故障诊断滤波器设计的解析解. 相似文献
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马尔可夫链在离散事件系统中的应用 总被引:2,自引:0,他引:2
离散事件系统是以事件驱动和状态不连续为特征的。因此,本文提出利用马尔可夫链来分析离散事件系统状态间的转移概率及稳态概率分布。 相似文献
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马尔可夫跳变线性系统(MJLS)是一种具有多个模态的随机系统,系统在各个模态之间的跳变转移由一组马尔可夫链来决定。MJLS模型因其在表示过程中可以产生突变而更能精确的描述实际工程应用中的系统。近年来,MJLS的最优控制问题成为了研究的热点,动态规划、极大值原理以及线性矩阵不等式等成为了解决此类问题的主流方法。本文对MJLS最优控制领域的研究现状进行了综述。分别对一般情况下、带有噪声的情况下、带有时滞的情况下以及某些特定情况下的MLJS最优控制问题的国内外研究现状进行论述。最后进行了总结并提出MJLS最优控制领域未来值得关注的研究方向。 相似文献
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本文研究了一类带有终端约束的切换系统在有限时间内的最优控制问题.终端约束的出现使得最优控制问题的值函数不再是处处可微的,甚至是不连续的.因此,原来关于无穷时间域上的值函数是Bensoussan-Lions拟变分不等式(QVI)的粘性解的这一结论已不再适用.本文采用了动态规划方法和生存定理将QVI的解延拓到了下半连续的情形,并且得到了有限时间最优切换控制问题的值函数是QVI的下半连续解的重要结论. 相似文献
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本文研究一类同时含有Markov跳过程和乘性噪声的离散时间非线性随机系统的最优控制问题, 给出并证明了相应的最大值原理. 首先, 利用条件期望的平滑性, 通过引入具有适应解的倒向随机差分方程, 给出了带有线性差分方程约束的线性泛函的表示形式, 并利用Riesz定理证明其唯一性. 其次, 对带Markov跳的非线性随机控制系统, 利用针状变分法, 对状态方程进行一阶变分, 获得其变分所满足的线性差分方程. 然后, 在引入Hamilton函数的基础上, 通过一对由倒向随机差分方程刻画的伴随方程, 给出并证明了带有Markov跳的离散时间非线性随机最优控制问题的最大值原理, 并给出该最优控制问题的一个充分条件和相应的Hamilton-Jacobi-Bellman方程. 最后, 通过
一个实际例子说明了所提理论的实用性和可行性. 相似文献
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M. Mariton 《Automatica》1987,23(6)
The notion of stochastic controllability for linear systems subject to Markovian jumps in parameter values is studied. An algebraic necessary and sufficient condition is obtained in terms of an easily computable rank test. 相似文献
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In this article, the problem of H 2-control of a discrete-time linear system subject to Markovian jumping and independent random perturbations is considered. Different H 2 performance criteria (often called H 2-norms) are introduced and characterised via solutions of some suitable linear equations on certain spaces of symmetric matrices. Some aspects specific to the discrete-time framework are revealed. The problem of optimisation of H 2-norms is solved under the assumption that full state vector is available for measurements. One shows that among all stabilising controllers of higher dimension, the best performance is achieved by a zero-order controller. The corresponding feedback gain of the optimal controller is constructed based on the stabilising solution of a system of discrete-time generalised Riccati equations. 相似文献
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This paper is concerned with the problem of asynchronous control for a class of discrete-time Markov systems with multiplicative stochastic white noises. Based on a stability analysis scheme developed from mode-dependent Lyapunov function method, we first derive testable conditions in linear matrix inequality (LMI) setting to ensure the robust stability of the closed-loop system. We then recast the proposed stability conditions into equivalent forms that are later utilised to design a multi-mode asynchronous state-feedback controller (ASFC) that makes the closed-loop system stable. An extension to the case of deficient mode information (i.e. transition rates of the system and the controller are not fully accessible) is also presented. Finally, a model of networked control with DC devices is given to demonstrate the efficacy of the proposed design scheme. 相似文献
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This article investigates the event‐triggered finite‐time reliable control problem for a class of Markovian jump systems with time‐varying transition probabilities, time‐varying actuator faults, and time‐varying delays. First, a Luenberger observer is constructed to estimate the unmeasured system state. Second, by applying an event‐triggered strategy from observer to controller, the frequency of transmission is reduced. Third, based on linear matrix inequality technique and stochastic finite‐time analysis, event‐triggered observer‐based controllers are designed and sufficient conditions are given, which ensure the finite‐time boundedness of the closed‐loop system in an H∞ sense. Finally, an example is utilized to show the effectiveness of the proposed controller design approach. 相似文献
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Zongli Lin 《国际强度与非线性控制杂志
》2017,27(17):3937-3950
》2017,27(17):3937-3950
This paper addresses the problem of robust stabilization for uncertain systems subject to input saturation and nonhomogeneous Markovian jumps, where the uncertainties are assumed to be norm bounded and the transition probabilities are time‐varying and unknown. By expressing the saturated linear feedback law on a convex hull of a group of auxiliary linear feedback laws and the time‐varying transition probabilities inside a polytope, we establish conditions under which the closed‐loop system is asymptotically stable. On the basis of these conditions, the problem of designing the state feedback gains for achieving fast transience response with a guaranteed size of the domain of attraction is formulated and solved as a constrained optimization problem with linear matrix inequality constraints. The results are then illustrated by numerical examples including the application to a DC motor speed control example. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
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We consider in this paper the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noises (MJLS-mn for short). Our objective is to present an optimal policy for the problem of maximising the system's total expected output over a finite-time horizon while restricting the weighted sum of its variance to a pre-specified upper-bound value. We obtain explicit conditions for the existence of an optimal control law for this problem as well as an algorithm for obtaining it, extending previous results in the literature. The paper is concluded by applying our results to a portfolio selection problem subject to regime switching. 相似文献