Inverse reinforcement learning for identification of linear–quadratic zero-sum differential games

In this paper, we address the inverse problem in the case of linear–quadratic zero-sum differential games. The problem is to evaluate an unknown cost function given the observed trajectories that are known to be generated by a stationary linear feedback Nash equilibrium pair. Using the observed data, we construct a game that is equivalent to the game that leads to the observed trajectories in the sense that the equilibrium feedback law of any of the two player is the same for that player in the original and constructed games. Towards this end, we introduce a model-based algorithm that uses the given trajectories to accomplish this task. The algorithm combines both inverse optimal control and reinforcement learning methods making extensive use of gradient descent optimization for the latter. The analysis of the algorithm focuses on the proof of its convergence and stability. Simulation results validate the effectiveness of the proposed algorithm