2024/07/14 by Santiago J. Leudo, Leudo, Santiago J., Ricardo G. Sanfelice +1
Computer Science · Decision Sciences · Engineering · #Artificial Intelligence in Games #FOS: Electrical engineering #FOS: Mathematics #Game Theory and Applications #Guidance and Control Systems #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2407.10107
openalex publication_date 2024/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we formulate a two-player zero-sum game under dynamic constraints defined by hybrid dynamical equations. The game consists of a min-max problem involving a cost functional that depends on the actions and resulting solutions to the hybrid system, defined as functions of hybrid time and, hence, can flow or jump. A terminal set conveniently defined allows to recast both finite and infinite horizon problems. We present sufficient conditions given in terms of Hamilton-Jacobi-Bellman-Isaacs-like equations to guarantee to attain a solution to the game. It is shown that when the players select the optimal strategy, the value function can be evaluated without computing solutions to the hybrid system. Under additional conditions, we show that the optimal state-feedback laws render a set of interest asymptotically stable for the resulting hybrid closed-loop system. Applications of these games, presented here as robust control problems, include disturbance rejection and security problems.