Adversarial Multi-agent Output Containment Graphical Game with Local and Global Objectives for UAVs

Abstract

Multiple leader & follower graphical games constitute challenging problems for aerospace and robotics applications. One of the challenges is to address the mutual interests among the followers with an optimal control point of view. In particular, the traditional approaches treat the output containment problem by introducing selfish followers where each follower only considers their own utility. In this paper, we propose a differential output containment game over directed graphs where the mutual interests among the followers are addressed with an objective functional that also considers the neighboring agents. The obtained output containment error system results in a formulation where outputs of all followers are proved to converge to the convex hull spanned by the outputs of leaders in a game optimal manner. The output containment problem is solved using the <inline-formula><tex-math notation="LaTeX">$\mathcal {H}_\infty$</tex-math></inline-formula> output feedback method where the new necessary and sufficient conditions are presented. Another challenge is to design distributed Nash equilibrium control strategies for such games, which cannot be achieved with the traditional quadratic cost functional formulation. Therefore, a modified cost functional that provides both Nash and distributed control strategies in the sense that each follower uses the state information of its own and neighbors, is presented. Furthermore, an <inline-formula><tex-math notation="LaTeX">$\mathcal {L}_{2}$</tex-math></inline-formula> gain bound of the output containment error system that experiences worst-case disturbances with respect to the <inline-formula><tex-math notation="LaTeX">$\mathcal {H}_\infty$</tex-math></inline-formula> criterion is investigated. The proposed methods are validated by means of multi-agent quadrotor Unmanned Aerial Vehicles (UAVs) output containment game simulations. IEEE