Solutions for Multiple-Defender Single-Attacker Convex Target Guarding Games: Verification via Parametric Optimization

• 成果类型: Article
• 署名作者: Lee, Yoonjae; Bakolas, Efstathios
• 署名单位: University of Texas System; University of Texas Austin
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3379948
• 发表日期: 2024
• 页码: 6357-6364
• 关键词: games; vectors; viscosity; optimization; differential games; Military aircraft; mathematical models; Agents and autonomous systems; parametric convex programming; pursuit-evasion games

摘要

A zero-sum differential game is considered in which a team of defenders is tasked with cooperatively capturing a single attacker who seeks to breach a convex region (or target). We show that the equilibrium strategies of the agents can be computed via a convex program, which remains tractable even in high-dimensional cases as opposed to the direct solution of the Hamilton-Jacobi-Isaacs (HJI) equation. To that end, we mainly attempt to prove the validity of a candidate for the value of the game constructed based on Isaacs' geometric approach using classical/viscosity solution concepts of the HJI equation. A major challenge is that the candidate value function generally lacks an analytical expression, making it difficult to derive its gradient/subdifferential. To address this challenge, we propose a parametric optimization approach to associate the candidate value function with the optimal value function of a parametric program and investigate its continuity and differentiability properties through duality and optimality conditions. Lastly, we present a numerical example to showcase the applicability of our solution in a nontrivial high-dimensional game scenario.