Adaptive dynamic programming-based design of integrated neural network structure for cooperative control of multiple MIMO nonlinear systems

Solving cooperative problems for multi-agent systems, in which the agent׳s artificial behaviors are similar to naturally biological behaviors of agents in practice, is a major challenge. The problems become more complex if the controlled agents are multi-input and multi-output (MIMO) nonlinear systems lacking knowledge of internal system dynamics and affected by external disturbances. In this paper, firstly, based on adaptive dynamic programming, three neural networks (NNs) (actor/disturber/critic) of control schemes for two-player games are integrated into the structure with only one NN, known as integrated NN (INN), with the aim of reducing computational complexity and waste of resources. Secondly, an INN weight update law and an online control algorithm, which updates parameters in one iterative step, are designed to find H∞ optimal cooperative control solutions. With the aid of Lyapunov theory, we prove that the INN weight approximation errors and the cooperative tracking errors are uniformly ultimately bounded (UUB), and the system parameters converge to the approximately optimal values. Finally, two simulation studies, one of which is compared to three-NN structures in existing literature, are carried out to show the effectiveness of the proposed INN structure.