Reinforcement learning for inverse linear-quadratic dynamic non-cooperative games

In this paper, we address the inverse problem in the case of linear-quadratic discrete-time dynamic non-cooperative games.Given feedback laws of players that are known to be a Nash equilibrium pair for a discrete-time linear system, we want find cost function parameters for which the observed feedback laws are optimal and stabilizing.Using the given feedback laws, we introduce a modelbased algorithm that generates cost function parameters solving the problem.We provide theoretical results that guarantee the convergence and stability of the algorithm as well as the way to generate new games with necessary properties without requiring to run the complete algorithm repeatedly .Then the algorithm is extended to a model-free version that uses data samples generated by unknown dynamics and has the same properties as the model-based version.Simulation results validate the effectiveness of the proposed algorithms.* ( ) = -( + ⊤) -1 ⊤ ( ( ) + ∑ ≠ * ( )).(10)