Model-Free Solution for Inverse Linear-Quadratic Nonzero-Sum Differential Games

This letter addresses the inverse problem for Linear-Quadratic (LQ) nonzero-sum N-player differential games, where the goal is to learn cost function parameters such that the given tuple of feedback laws, which is known to stabilize a linear system, is a Nash equilibrium (NE) for the synthesized game. We show a model-free algorithm that can accomplish this task using the given feedback laws and the system matrices. The algorithm makes extensive use of gradient descent optimization that allow to find the solution to the inverse problem without solving the forward problem. To further illustrate possible solution characterization, we show how to generate an infinite number of equivalent games without repeatedly running the complete algorithm. Simulation results demonstrate the effectiveness of the proposed algorithms.