{"title":"Adaptive dynamic programming for containment control with robustness analysis to iterative error: A global Nash equilibrium solution","authors":"Zitao Chen , Kairui Chen , Jianhui Wang","doi":"10.1016/j.isatra.2024.08.024","DOIUrl":null,"url":null,"abstract":"<div><div>Global Nash equilibrium is an optimal solution for each player in a graphical game. This paper proposes an iterative adaptive dynamic programming-based algorithm to solve the global Nash equilibrium solution for optimal containment control problem with robustness analysis to the iterative error. The containment control problem is transferred into the graphical game formulation. Sufficient conditions are given to decouple the Hamilton–Jacobi equations, which guarantee the solvability of the global Nash equilibrium solution. The iterative algorithm is designed to obtain the solution without any knowledge of system dynamics. Conditions of iterative error for global stability are given with rigorous proof. Compared with existing works, the design procedures of control gain and coupling strength are separated, which avoids trivial cases in the design procedure. The robustness analysis exactly quantifies the effect of the iterative error caused by various sources in engineering practice. The theoretical results are validated by two numerical examples with marginally stable and unstable dynamics of the leader.</div></div>","PeriodicalId":14660,"journal":{"name":"ISA transactions","volume":"154 ","pages":"Pages 132-146"},"PeriodicalIF":6.3000,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ISA transactions","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0019057824004075","RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
Global Nash equilibrium is an optimal solution for each player in a graphical game. This paper proposes an iterative adaptive dynamic programming-based algorithm to solve the global Nash equilibrium solution for optimal containment control problem with robustness analysis to the iterative error. The containment control problem is transferred into the graphical game formulation. Sufficient conditions are given to decouple the Hamilton–Jacobi equations, which guarantee the solvability of the global Nash equilibrium solution. The iterative algorithm is designed to obtain the solution without any knowledge of system dynamics. Conditions of iterative error for global stability are given with rigorous proof. Compared with existing works, the design procedures of control gain and coupling strength are separated, which avoids trivial cases in the design procedure. The robustness analysis exactly quantifies the effect of the iterative error caused by various sources in engineering practice. The theoretical results are validated by two numerical examples with marginally stable and unstable dynamics of the leader.
期刊介绍:
ISA Transactions serves as a platform for showcasing advancements in measurement and automation, catering to both industrial practitioners and applied researchers. It covers a wide array of topics within measurement, including sensors, signal processing, data analysis, and fault detection, supported by techniques such as artificial intelligence and communication systems. Automation topics encompass control strategies, modelling, system reliability, and maintenance, alongside optimization and human-machine interaction. The journal targets research and development professionals in control systems, process instrumentation, and automation from academia and industry.