Nash Equilibrium Verification of Inverse Linear-Quadratic Differential Games Over Networks

This paper considers Nash equilibrium verification problem of inverse linear-quadratic (LQ) differential games, which answers the question whether a set of controllers constitutes a Nash equilibrium of a LQ differential game. This establishes a solid foundation for inverse differential games where performance indices can be identified through controllers. Distributed verification criteria are established via geometric characterization of constrained algebraic Riccati equation solutions, and can be easily checked from system dynamics and given feedback matrices. Moreover, an analytical reconstruction method is proposed for the corresponding state weighting matrices in the LQ performance indices.