Non‐zero‐sum games of discrete‐time Markov jump systems with unknown dynamics: An off‐policy reinforcement learning method

Abstract

This article concentrates on the non‐zero‐sum games problem of discrete‐time Markov jump systems without requiring the system dynamics information. First, the multiplayer non‐zero‐sum games problem can be converted to solve a set of coupled game algebraic Riccati equations, which is difficult to be solved directly. Then, to obtain the optimal control policies, a model‐based algorithm adapting the policy iteration approach is proposed. However, the model‐based algorithm relies on system dynamics information, which has the limitations in practice. Subsequently, an off‐policy reinforcement learning algorithm is given to get rid of the dependence on system dynamics information, which only uses the information of system states and inputs. Moreover, the proof of convergence and Nash equilibrium are also given. Finally, a numerical example is given to demonstrate the effectiveness of the proposed algorithms.

Multi‐event‐triggered adaptive dynamic programming for non‐zero‐sum game of unknown nonlinear system

“…Then, the relevant NZSG problems under adaptive dynamic programming (ADP) were studied. [3][4][5] Liu et al 6 came up with a unique online technique for multi-player NZSGs of nonlinear partially unknown continuous-time systems with control constraints developed based on NNs. Wang et al 7 designed a specific cost function related to tracking errors and their derivatives to solve NZSG problem of continuous-time plants via ADP.…”