吉林大学学报(工学版) ›› 2024, Vol. 54 ›› Issue (3): 828-835.doi: 10.13229/j.cnki.jdxbgxb.20220538

• 通信与控制工程 • 上一篇    

不依赖观测器的不确定性系统输出反馈鲁棒控制

赵军1(),赵子亮2(),朱庆林2,郭斌2   

  1. 1.山东科技大学 机械电子工程学院,山东 青岛 266590
    2.山东科技大学 交通学院,山东 青岛 266590
  • 收稿日期:2022-05-08 出版日期:2024-03-01 发布日期:2024-04-18
  • 通讯作者: 赵子亮 E-mail:junzhao1993@163.com;zhaoziliang1@sdust.edu.cn
  • 作者简介:赵军(1993-),男,教授,博士.研究方向:非线性系统最优/鲁棒控制.E-mail:junzhao1993@163.com
  • 基金资助:
    国家自然科学基金项目(62203279);山东省自然科学基金项目(ZR2022QF011)

Output⁃feedback robust control of uncertain systems without observer

Jun ZHAO1(),Zi-liang ZHAO2(),Qing-lin ZHU2,Bin GUO2   

  1. 1.College of Mechanical and Electronic Engineering,Shandong University of Science and Technology,Qingdao 266590,China
    2.College of Transportation,Shandong University of Science and Technology,Qingdao 266590,China
  • Received:2022-05-08 Online:2024-03-01 Published:2024-04-18
  • Contact: Zi-liang ZHAO E-mail:junzhao1993@163.com;zhaoziliang1@sdust.edu.cn

摘要:

针对非匹配不确定性系统的静态输出反馈鲁棒控制问题在线求解难的难题,提出了一种基于数据驱动学习的自适应学习算法。首先,将不确定性系统的鲁棒控制问题转化为具有性能指标函数的标称系统的最优控制问题。其次,为实现输出反馈最优控制,根据状态反馈控制项构造了输出反馈黎卡提方程。再次,为实现该输出反馈黎卡提方程的在线求解,使用克罗内克积和向量化操作重构输出反馈黎卡提方程,进而设计了基于输入/输出数据的自适应学习算法,摒弃了传统观测器的使用,实现可一步求解的输出反馈鲁棒控制。最后,为实现被估参数的快速收敛,进一步放松了所要求的持续激励条件。仿真结果验证了本文控制方法和学习算法的有效性。

关键词: 控制理论与控制工程, 数据驱动学习, 鲁棒控制, 最优控制, 持续激励条件

Abstract:

A novel data-driven learning method to achieve static output-feedback robust control of unmatched dynamic systems was proposed, which uses the techniques originally developed for optimal control. The robust control was first transformed into the optimal control of an augmented system, taking unmatched dynamics into consideration. Then, to design the output-feedback optimal control, an output-feedback algebraic Riccati equation was derived by tailoring its state-feedback control counterpart. Once more, an adaptive online learning method was designed to avoid using the observer, where two operations (i.e., vectorization and Kronecker's product) were adopted to reconstruct the output-feedback algebraic Riccati equation. Finally, the required persistent excitation condition was further relaxed to realize the rapid convergence of the estimated parameters. Simulation results show the effectiveness of the proposed control method and learning algorithm.

Key words: control theory and control engineering, data-driven learning, robust control, optimal control, persistent excitation condition

中图分类号: 

  • TP13

图1

本文学习算法与文献[15]算法分别对输出反馈黎卡提方程求解"

图2

估计误差P*-P^的范数"

图3

系统控制输入"

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