Policy iteration for H∞ control of polynomial time-varying systems

IF 2.2 4区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS IET Control Theory and Applications Pub Date : 2024-04-12 DOI:10.1049/cth2.12661

Sajjad Pakkhesal, Saeed Shamaghdari

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Abstract

This paper studies the H_∞ control problem for polynomial time-varying systems. The H_∞ control problem has been much less investigated for time-varying systems in comparison to the time-invariant systems. Approximate dynamic programming (ADP) is an optimal method to solve the control problems. Therefore, it is valuable to solve the polynomial time-varying H_∞ control problem with the ADP approach. Considering the time as an independent variable for sum-of-squares (SOS) optimization problems, an SOS-based ADP method is proposed to solve this problem. A policy iteration algorithm is presented, where in its policy evaluation step it is sufficient to solve an optimization problem. Some constraints are added to this optimization problem to guarantee the closed-loop exponential stability. The convergence and stability properties of the proposed algorithm are stated and proven. Moreover, in order to design an H_∞ controller with a smaller disturbance attenuation coefficient, a two-loop algorithm is suggested. Finally, the effectiveness of the proposed method is demonstrated by simulation examples.

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多项式时变系统 H∞ 控制的策略迭代

本文研究多项式时变系统的 H∞ 控制问题。与时变系统相比，对时变系统的 H∞ 控制问题的研究要少得多。近似动态编程（ADP）是解决控制问题的最佳方法。因此，用 ADP 方法求解多项式时变 H∞ 控制问题很有价值。考虑到时间是平方和（SOS）优化问题的自变量，提出了一种基于 SOS 的 ADP 方法来解决这一问题。提出了一种策略迭代算法，在其策略评估步骤中，只需解决一个优化问题即可。为保证闭环指数稳定性，在该优化问题中添加了一些约束条件。提出并证明了所提算法的收敛性和稳定性。此外，为了设计扰动衰减系数更小的 H∞ 控制器，提出了一种双环算法。最后，通过仿真实例证明了所提方法的有效性。

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来源期刊

IET Control Theory and Applications 工程技术-工程：电子与电气

CiteScore

5.70

自引率

7.70%

发文量

167

审稿时长

5.1 months

期刊介绍： IET Control Theory & Applications is devoted to control systems in the broadest sense, covering new theoretical results and the applications of new and established control methods. Among the topics of interest are system modelling, identification and simulation, the analysis and design of control systems (including computer-aided design), and practical implementation. The scope encompasses technological, economic, physiological (biomedical) and other systems, including man-machine interfaces. Most of the papers published deal with original work from industrial and government laboratories and universities, but subject reviews and tutorial expositions of current methods are welcomed. Correspondence discussing published papers is also welcomed. Applications papers need not necessarily involve new theory. Papers which describe new realisations of established methods, or control techniques applied in a novel situation, or practical studies which compare various designs, would be of interest. Of particular value are theoretical papers which discuss the applicability of new work or applications which engender new theoretical applications.