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Markov跳变系统滚动时域有限记忆控制

闻继伟, 刘飞   

  1. 江南大学自动化研究所, 无锡 214122
  • 收稿日期:2008-07-25 修回日期:2009-04-20 出版日期:2010-07-25 发布日期:2010-07-25

闻继伟;刘飞. Markov跳变系统滚动时域有限记忆控制[J]. 系统科学与数学, 2010, 30(7): 911-921.

WEN Jiwei;LIU Fei. Receding Horizon Finite Memory Control for Markov Jump Systems[J]. Journal of Systems Science and Mathematical Sciences, 2010, 30(7): 911-921.

Receding Horizon Finite Memory Control for Markov Jump Systems

WEN Jiwei, LIU Fei   

  1. Institute of Automation, Jiangnan University, Wuxi 214122
  • Received:2008-07-25 Revised:2009-04-20 Online:2010-07-25 Published:2010-07-25
针对离散时间Markov跳变系统,提出滚动时域有限记忆控制的方法.在一段有限滤波时域上,利用系统输入与输出变量的线性组合构造一段有限控制时域上的输出反馈控制器.首先,不考虑跳变系统均方可镇定,基于最优控制的方法,获得以迭代计算形式给出的控制器,并使其在无偏条件下能优化二次型性能指标.其次,进一步考虑在成本衰减条件下确定终端加权矩阵,并以它作为边界条件计算得到最优控制律,调节系统均方稳定.为便于求解,成本衰减条件以线性矩阵不等式的形式给出.仿真实例验证了所提方法的可行性和有效性.
This paper is concerned with the problem of receding horizon finite memory control (RHFMC) for discrete-time Markov jump linear systems. The aim is to find an output feedback control with a finite memory structure which can be represented by linear combination of outputs and inputs during a finite filter horizon. First, RHFMC with an iterative form is obtained while minimizing a quadratic performance index defined on a finite control horizon under an unbiased condition. Due to the difficulty of stability guarantee, then the above mentioned RHFMC is improved by determining terminal weighting matrix which satisfies cost monotonicity
condition. The control law calculated by using this kind of terminal weighting matrix as boundary condition naturally guarantees the mean square stability of the closed-loop system. A sufficient condition for the existence of the terminal weighting matrix is presented in linear matrix inequality (LMI) form. Finally, a
numerical example is given to illustrate the effectiveness of the proposed method.

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[1] 林文娟,何勇. 部分转移概率未知的时滞离散Markov跳变系统可达集估计[J]. 系统科学与数学, 2019, 39(2): 298-310.
[2] 黄玲,孙敏. 区间时变时滞Markov跳变系统的一种改进稳定性分析方法[J]. 系统科学与数学, 2016, 36(7): 995-1005.
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