Decentralized adaptive optimal stabilization of nonlinear systems with matched interconnections

In this paper, we investigate the decentralized feedback stabilization and adaptive dynamic programming (ADP)-based optimization for the class of nonlinear systems with matched interconnections. The decentralized control law of the overall system is designed by integrating all controllers of the isolated subsystems, and it satisfies the optimality on the basis of optimal control laws of all the subsystems. For solving the optimal control problems of these isolated subsystems, the policy iteration algorithm is used to approximately solve the Hamilton-Jacobi-Bellman equations in the framework of ADP with the neural network implementation, where a set of critic neural networks is constructed to estimate the optimal cost functions, and the approximate optimal control laws can be obtained after the learning of critic neural networks. The weight estimation errors of the critic networks and the stability of all isolated subsystems are proved based on the Lyapunov theory. Finally, the performance of the proposed decentralized optimal control strategy is verified by simulation results.