Solution Sets for Inverse Non-Cooperative Linear-Quadratic Differential Games

This letter 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.