A learning optimal control scheme for robust stabilization of a class of uncertain nonlinear systems

In this paper, a novel learning optimal control scheme is established to design the robust controller of a class of uncertain nonlinear systems. The robust control problem is transformed into the optimal control problem by properly choosing a cost function that reflects the uncertainty, regulation, and control. Then, the online policy iteration algorithm is presented to solve the Hamilton-Jacobi-Bellman (HJB) equation by introducing a critic neural network. The approximate expression of the optimal control policy can be derived directly. Moreover, the closed-loop system is proved to be uniformly ultimately bounded. The equivalence of the neural-network-based HJB solution of the optimal control problem and the solution of the robust control problem is developed as well. Finally, an example is provided to verify the effectiveness of the constructed approach.