A neural-network-based online optimal control approach for nonlinear robust decentralized stabilization

In this paper, the robust decentralized stabilization of continuous-time uncertain nonlinear systems with multi control stations is developed using a neural network based online optimal control approach. The novelty lies in that the well-known adaptive dynamic programming method is extended to deal with the nonlinear feedback control problem under uncertain and large-scale environment. Through introducing an appropriate bounded function and defining a modified cost function, it can be observed that the decentralized optimal controller of the nominal system can achieve robust decentralized stabilization of original uncertain system. Then, a critic neural network is constructed for solving the modified Hamilton–Jacobi–Bellman equation corresponding to the nominal system in an online fashion. The weights of the critic network are tuned based on the standard steepest descent algorithm with an additional term provided to guarantee the boundedness of system states. The stability analysis of the closed-loop system is carried out via the Lyapunov approach. At last, two simulation examples are given to verify the effectiveness of the present control approach.