广东工业大学学报 ›› 2022, Vol. 39 ›› Issue (05): 46-51,60.doi: 10.12052/gdutxb.220045

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时变发射概率影响下模态受限线性跳变系统非同步控制

张林闯, 杜欣烨, 金洪洪, 周伟, 孙永辉   

  1. 河海大学 能源与电气学院，江苏 南京 210098
  • 收稿日期:2022-03-14 发布日期:2022-07-18
  • 通信作者: 孙永辉(1980–)，男，教授，博士，博士生导师，主要研究方向为随机系统分析与控制、综合能源系统优化调度，E-mail：sunyonghui168@gmail.com
  • 作者简介:张林闯(1993–)，男，博士研究生，主要研究方向为随机系统分析与控制
  • 基金资助:
    国家自然科学基金资助项目 (62073121)；中央高校基本科研业务费专项资金资助项目 (B210203050)；江苏省研究生科研与实践创新计划项目 (KYCX21_0472)

Asynchronous Control of Mode-constrained Linear Jump Systems with Time-varying Emission Probability

Zhang Lin-chuang, Du Xin-ye, Jin Hong-hong, Zhou Wei, Sun Yong-hui   

  1. College of Energy and Electrical Engineering, Hohai University, Nanjing 210098, China
  • Received:2022-03-14 Published:2022-07-18

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摘要： 针对一类模态受限的线性跳变系统，研究基于时变发射概率方法的非同步控制问题。首先，考虑外界环境因素导致实际系统产生参数、结构变化的现象，引入semi-Markov跳变系统模型描述此类线性跳变系统的状态变化。考虑系统的模态受限现象，使用隐semi-Markov转移概率模型与时变发射概率模型分别描述系统的模态变化以及系统与控制器之间的模态关系。然后，构造非同步静态输出反馈控制器以保障系统的稳定运行。此外，基于Lyapunov稳定性理论与线性矩阵不等式方法，给出闭环线性跳变系统的随机稳定性条件以及控制器存在条件。与传统的基于时不变发射概率的非同步控制方法相比，本文所提的非同步静态输出反馈控制策略能够极大地降低保守性。最后，通过数值仿真算例验证所提非同步静态输出反馈控制器的有效性与正确性。

关键词: 模态受限线性跳变系统, semi-Markov跳变系统模型, 非同步输出反馈控制, 时变发射概率方法

Abstract: The asynchronous control problem based on time-varying emission probability approach is studied for a class of mode-constrained linear jump systems. Firstly, considering the parameter and structure change of the actual system affected by external environmental factor, the semi-Markov jump system model is introduced to characterize the state change of this class of systems. Considering the mode constraints of the system, the hidden semi-Markov transition rates model and time-varying emission probability model are used to describe the mode changes of the system and the mode relationship between the system and the controller, respectively. Furthermore, an asynchronous static output feedback controller is constructed to ensure the stable operation of the system. In addition, based on Lyapunov stability theory and linear matrix inequality method, the stochastic stability conditions and the existence conditions of the controller for the closed-loop linear jump system are given. Compared with the traditional asynchronous control method based on time-invariant emission probability, the proposed asynchronous static output feedback control strategy can greatly reduce the conservatism. Finally, a numerical example is given to verify the effectiveness and correctness of the proposed asynchronous static output feedback controller.

Key words: mode-constrainted linear jump systems, semi-Markov jump system model, asynchronous output feedback control, time-varying emission probability approach

中图分类号: 

  • TG156
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