Robust optimal control for a class of nonlinear dynamic systems using single network adaptive dynamic programming

In this paper, the robust optimal control for a class of nonlinear systems with uncertainties is investigated by using single network adaptive dynamic programming approach. The robust controller of the original uncertain nonlinear system is derived by adding a feedback gain to the optimal controller of the nominal system. It is proved that the robust controller can achieve optimality under a specified cost function. Then, a single neural network is constructed for solving the Hamilton-Jacobi-Bellman equation corresponding to the nominal system, where an additional stabilizing term is introduced to check the stability. Furthermore, the obtained results are extended to establish the decentralized optimal control strategy for a class of nonlinear interconnected large-scale systems. Finally, a simulation example is provided to illustrate the effectiveness of the control scheme.