Policy iteration based cooperative linear quadratic differential games with unknown dynamics

Abstract

This article investigates the Pareto optimality of infinite horizon cooperative linear quadratic (LQ) differential games by policy iteration technique where the system dynamics are partially or completely unknown. Firstly, the policy iteration algorithm for the approximate solutions of the corresponding algebraic Riccati equation (ARE) without any prior knowledge of the matrix parameters of the dynamic system is derived by collecting the input and state information of each player. Secondly, when the presented specific rank condition is satisfied, the convergence of the proposed algorithm is rigorously demonstrated by recursion. Moreover, the weighting approach is employed to obtain the Pareto optimal strategy and the Pareto optimal solutions on the basis of the convex optimization theory. Finally, simulation results are reported to verify the feasibility and correctness of the proposed theoretical results.