Robust stabilization of discrete-time uncertain nonlinear systems using neuro-optimal control strategy

In this paper, the robust stabilization problem for a class of discrete-time uncertain nonlinear systems is investigated by using a neuro-optimal control strategy. The robust stabilization problem is converted into an optimal control problem under some proper conditions. Then, in order to deal with the transformed optimal control problem, the discrete-time generalized Hamilton-Jacobi-Bellman equation is introduced and solved by employing the successive approximation method. The convergence proof of the iterative algorithm and the design procedure of the neural network implementation are developed as well. A numerical simulation is also provided to illustrate the effectiveness of the control strategy.