Based on the Lyapunov stability theorem, a design methodology of adaptive block backstepping controller is proposed in this thesis for a class of multi-input systems with mismatched perturbations to solve regulation problems. According to the number of block (m) in the plant to be controlled, m-1 virtual input controllers are designed from the first block to the (m-1)th block. Then the proposed robust controller is designed from the last block. Adaptive mechanisms are employed in each of the virtual input controllers as well as the robust controller, so that the knowledge of the least upper bounds of mismatched perturbations is not required. The resultant control system can achieve asymptotic stability. Finally, a numerical example and a practical example are given for demonstrating the feasibility of the proposed control scheme.

A methodology of designing an adaptive sliding mode controller for a class of nonlinear systems with matched and mismatched perturbations is proposed in this thesis. A specific designed sliding surface function is presented first, whose coefficients are determined by using Lyapunov stability theorem and linear matrix inequality (LMI) optimization technique. Without requiring the upper bounds of matched perturbations, the controller with adaptive mechanisms embedded is also designed by using Lyapunov stability theorem. The proposed control scheme not only can drive the trajectories of the controlled systems reach sliding surface in finite time, but also is able to suppress the mismatched perturbations when the controlled systems are in the sliding mode, and achieve asymptotic stability. In addition, the proposed control scheme can be directly applied to a class of underactuated systems. A numerical example and a practical experiment are given for demonstrating the feasibility of the proposed control scheme.