东北大学学报（自然科学版）

东北大学学报（自然科学版） ›› 2021, Vol. 42 ›› Issue (2): 160-165.DOI: 10.12068/j.issn.1005-3026.2021.02.002

• 信息与控制 • 上一篇    下一篇

马尔科夫跳变系统的H∞-自适应变结构控制

杨冬梅， 鹿笛   

  1. (东北大学 理学院， 辽宁 沈阳110819)
  • 发布日期:2021-03-05
  • 通讯作者: 杨冬梅
  • 作者简介:杨冬梅(1966-)，女，辽宁沈阳人，东北大学教授.
  • 基金资助:
    国家自然科学基金资助项目(61673100).

H∞-Adaptive Variable Structure Control Based on Markov Jump Systems

YANG Dong-mei， LU Di   

  1. School of Sciences， Northeastern University， Shenyang 110819， China.
  • Published:2021-03-05
  • Contact: LU Di
  • About author:-
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摘要： 研究了一类带有一般不确定转移速率的非线性广义时滞马尔科夫跳变系统的H∞-自适应变结构控制问题.首先，针对系统中的非线性未知参数设计由线性控制器和自适应控制器组成的混合控制器，构建Lyapunov泛函，使得系统的轨迹趋近于状态空间曲面且闭环系统随机容许，满足H∞性能γ.进而考虑一般不确定转移速率矩阵的特性，构造严格线性矩阵不等式，使结论更具一般性.最后，通过数值算例及图像仿真验证了这类控制方法的有效性和可行性.

关键词: 马尔科夫跳变系统;广义系统;自适应变结构控制;H∞性能

Abstract: The control problem for a class of nonlinear generalized delay Markov jump systems with generally uncertain transition rate is studied. First， a hybrid controller composed of a linear controller and an adaptive controller is designed for the unknown nonlinear parameters in the system， and a Lyapunov functional is constructed to make the trajectory of the system approach to the state space surface and the closed-loop system is admissible， satisfying H∞criteria γ. Furthermore， considering the characteristics of the generally uncertain transition rates matrices， a strict linear matrix inequality is constructed to make the conclusion more general. Finally， the effectiveness and feasibility of this control method are verified by numerical examples and image simulation.

Key words: Markov jump system; singular system; adaptive variable structure control; H∞performance

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