Neural-network-based robust optimal control design for a class of uncertain nonlinear systems via adaptive dynamic programming

Abstract

In this paper, the neural-network-based robust optimal control design for a class of uncertain nonlinear systems via adaptive dynamic programming approach is investigated. First, the robust controller of the original uncertain system is derived by adding a feedback gain to the optimal controller of the nominal system. It is also shown that this robust controller can achieve optimality under a specified cost function, which serves as the basic idea of the robust optimal control design. Then, a critic network is constructed to solve the Hamilton–Jacobi–Bellman equation corresponding to the nominal system, where an additional stabilizing term is introduced to verify the stability. The uniform ultimate boundedness of the closed-loop system is also proved by using the Lyapunov approach. Moreover, the obtained results are extended to solve decentralized optimal control problem of continuous-time nonlinear interconnected large-scale systems. Finally, two simulation examples are presented to illustrate the effectiveness of the established control scheme.