Nash Equilibria for Linear Quadratic Discrete-Time Dynamic Games via Iterative and Data-Driven Algorithms

• 成果类型: Article
• 署名作者: Nortmann, Benita; Monti, Andrea; Sassano, Mario; Mylvaganam, Thulasi
• 署名单位: Imperial College London; Helmholtz Association; German Aerospace Centre (DLR)
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3375249
• 发表日期: 2024
• 页码: 6561-6575
• 关键词: games; Nash equilibrium; Heuristic algorithms; COSTS; CONVERGENCE; Iterative algorithms; aerodynamics; game theory; Linear systems; optimization algorithms; data-driven methods

摘要

Determining feedback Nash equilibrium solutions of nonzero-sum dynamic games is generally challenging. In this article, we propose four different iterative algorithms to find Nash equilibrium strategies for discrete-time linear quadratic games. The strategy update laws are based on the solution of either Lyapunov or Riccati equations for each player. Local convergence criteria are discussed. Motivated by the fact that in many practical scenarios each player in the game may have access to different (incomplete) information, we also introduce purely data-driven implementations of the algorithms. This allows the players to reach a Nash equilibrium solution of the game via scheduled experiments and without knowledge of each other's performance criteria or of the system dynamics. The efficacy of the presented algorithms is illustrated via numerical examples and a practical example involving human-robot interaction.