Design of adaptive block backstepping controllers for uncertain nonlinear dynamic systems with n blocks

Based on the Lyapunov stability theorem, a design methodology of adaptive block backstepping control is proposed in this article for a class of multi-input systems with matched and mismatched perturbations to solve regulation problems. The systems to be controlled contain n blocks' dynamic equations, hence n???1 virtual input controllers are firstly designed so that the state variables of first n???1 blocks are asymptotically stable if each virtual control input is equal to the state variable of next block. Then the control input is designed in the last nth block to ensure asymptotic stability for the whole state variables even if the perturbations exist. In addition, adaptive mechanisms are embedded in each virtual input function and control input, so that the upper bound of perturbations is not required to be known beforehand. Finally, a numerical example is given for demonstrating the feasibility of the proposed control scheme.