Optimality and Asymptotic Stability in Two-Player Zero-Sum Hybrid Games

In this work, we formulate a two-player zero-sum game under dynamic constraints given in terms of hybrid dynamical systems. Find the full version in [8], including the main results and outlines of the corresponding proofs. We propose sufficient conditions to guarantee attaining a solution to the game. When the players select the optimal strategy, the value function can be evaluated without the need of computing solutions. Under additional conditions, the optimal feedback laws render a set of interest asymptotically stable. Using this framework, we address an optimal control problem under the presence of an adversarial action in which the decision-making agents have dynamics that might exhibit both continuous and discrete behavior.