Inverse Nested Differential Games: Solvability, Stability and Identification

This paper considers for the first time the inverse nested differential game (INDG) problem for a class of network nonlinear systems. Such a nested game is composed of zero-sum games between controllers and external inputs in subsystems and a graphical game between subsystems. INDG answers the question that whether a set of given controllers constitutes a Nash equilibrium, and how to design meaningful performance indexes for an inverse nested game. Firstly, sufficient criteria of INDG are proposed, based on which an analytical relationship among performance indexes, distributed controllers, and control Lyapunov functions is revealed; Secondly, the stability of the network system is rigorously proved under the reconstructed performance indexes and given controllers; Finally, INDG is exploited to the strict-feedback form system where the INDG-based distributed optimal identification is explicitly accomplished.