Backstepping-based adaptive predictive optimal control of nonlinear systems with application to missile–target engagement

In this paper, an adaptive predictive optimal control scheme for a class of block strict-feedback nonlinear systems is proposed by integrating the adaptive dynamic programming (ADP) technique, predictive control and backstepping method. The basic idea is that designing the virtual and actual controls of backstepping is the optimized solutions of corresponding subsystems. Firstly, the virtual control input is derived for the subsystem by utilizing ADP technique, in which a critic neural network (NN) is constructed to approximate the solution of the associated Hamilton–Jacobi–Bellman (HJB) equation. Then, to further reduce the computational complexity, the actual controller is given in an analytical form by using continuous-time predictive approach. Theoretical analysis guarantees the stability of the closed-loop system by Lyapunov method. Finally, the effectiveness of the proposed adaptive predictive optimal control scheme is validated through an application to missile–target engagement.