Data-driven adaptive dynamic programming schemes for non-zero-sum games of unknown discrete-time nonlinear systems

Abstract

Abstract This paper integrates game theory, optimal control theory and reinforcement learning to deal with the discrete-time (DT) multi-player non-zero-sum game issue. As is known, the solutions to non-zero-sum game problems are the outcomes of coupled Riccati equations or coupled Hamilton–Jacobi ones, which are generally difficult to solve analytically and require the knowledge of accurate system mathematical models. However, for most practical industrial systems, the system dynamics cannot be obtained accurately or even unavailable, and the conventional model-based methods will be invalid. To overcome this deficiency, we develop data-based adaptive dynamic programming (ADP) algorithms for completely unknown multi-player systems. Firstly, the Nash equilibrium and stationarity conditions are used to formulate the DT multi-player non-zero-sum game, and then policy iteration algorithm is applied to approximate optimal solutions successively. Secondly, a novel online ADP algorithm combined with a neural-network-based identification scheme is designed and only requires the system data instead of the real system models. Subsequently, a data-driven action-dependent heuristic dynamic programming approach is presented and circumvents the estimation errors caused by the identification learning procedure. Finally, two simulation examples are provided to illustrate the feasibility of our schemes.