Adversarial Multi-agent Leader-Follower Graphical Game with Local and Global Objectives

Multiple leader and follower graphical games constitute challenging problems for aerospace and robotics applications. One of the challenges arises from having a different number of followers and leaders. We overcome this by employing an output containment error system that results in a formulation where outputs of all followers are proved to converge the convex hull spanned by the outputs of leaders. Another challenge is to design distributed Nash equilibrium control strategies for such games, which cannot be achieved with 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 ${{\mathcal{L}}_2}$ gain bound of the output containment error system that experiences unbounded disturbances is investigated by a recently developed class of digraphs that results in a semi-simple pinned graph Laplacian.