Backstepping-based adaptive dynamic programming for missile-target guidance systems with state and input constraints

In this paper, a novel backstepping-based adaptive dynamic programming (ADP) method is developed to solve the problem of intercepting a maneuver target in the presence of full-state and input constraints. To address state constraints, a barrier Lyapunov function is introduced to every backstepping procedure. An auxiliary design system is employed to compensate the input constraints. Then, an adaptive backstepping feedforward control strategy is designed, by which the tracking problem for strict-feedback systems can be reduced to an equivalence optimal regulation problem for affine nonlinear systems. Secondly, an adaptive optimal controller is developed by using ADP technique, in which a critic network is constructed to approximate the solution of the associated Hamilton–Jacobi–Bellman (HJB) equation. Therefore, the whole control scheme consists of an adaptive feedforward controller and an optimal feedback controller. By utilizing Lyapunov's direct method, all signals in the closed-loop system are guaranteed to be uniformly ultimately bounded (UUB). Finally, the effectiveness of the proposed strategy is demonstrated by using a simple nonlinear system and a nonlinear two-dimensional missile-target interception system.