Adaptive learning solution of the nonzero-sum differential game with unknown dynamics using adaptive dynamic programming
Chunbin Qin, Hongfei Sun, Xianxing Liu, Jiaqi Chen · 2016
In this paper, a novel partially model-free adaptive dynamic programming (ADP) algorithm is presented to solve online the nonzero-sum differential games of continuous-time linear systems with unknown drift dynamics. Firstly, by using the integral reinforcement learning technique, the partially model-free ADP algorithm is developed to solve online the set of coupled algebraic Riccati equation (ARE) underlying the game problem without the requirement of the complete knowledge of the system dynamics. And then, the convergence of the partially model-free ADP algorithm is proved by demonstrating that it is mathematically equivalent to the extended Kleiman's algorithm, previously proposed in the literature, that solves in an offline sense the set of coupled algebraic Riccati equation using the complete knowledge of the system dynamics. Finally, one example is given to demonstrate the efficiency of the proposed algorithm.