Design of adaptive block backstepping controllers for semi-strict feedback nonlinear systems with perturbation estimation

Based on the Lyapunov stability theorem, a design methodology of adaptive block backstepping control with perturbation estimation scheme is proposed in this paper for a class of multi-input systems with perturbations to solve regulation problems. First of all, the virtual input controllers are designed from the first block to the (m-1)th block. Then the proposed robust controller and the perturbation estimator are designed in accordance with the last block. Adaptive mechanisms are employed in each of the virtual input as well as the robust controller so that they may automatically adapt the least upper bounds of perturbations or perturbation estimation errors which may not fulfill the strict-feedback form. Furthermore, the proposed control scheme is able to achieve asymptotic stability. A numerical example is also given for demonstrating the feasibility of the proposed control scheme.