We consider the problem of computing parameters of player cost functionals such that given state and control trajectories constitute an open-loop Nash equilibrium for a noncooperative differential game. We propose two methods for solving this inverse differential game problem and novel conditions under which our methods compute unique cost-functional parameters. Our conditions are analogous to persistence of excitation conditions in adaptive control and parameter estimation. The efficacy of our methods is illustrated in simulations. Index Terms-Game theory, inverse differential games, inverse optimal control, optimal control.
This paper addresses the inverse problem of differential games, where the aim is to compute cost functions which lead to observed Nash equilibrium trajectories. The solution of this problem allows the generation of a model for inferring the intent of several agents interacting with each other. We present a method to find all cost functions which lead to the same Nash equilibrium in an infinite-horizon LQ differential game. The approach relies on a reformulation of the coupled matrix Riccati equations which arise out of necessary and sufficient conditions for Nash equilibria. Furthermore, based on our findings, we present an approach to compute a solution given a set of observed state and control trajectories. Our results highlight properties of feedback Nash equilibria in LQ differential games and provide an efficient approach for the estimation of cost function matrices in such a scenario.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.