Design of Adaptive Variable Structure Tracking Controllers for a Class of Systems with Nonholonomic Constraints

Based on the Lyapunov stability theorem, a design methodology of adaptive variable structure tracking controller is proposed in this paper for a class of perturbed nonlinear systems with nonholonomic constraints to solve the trajectory tracking control problems. In the first stage, the nonhomogeneous dynamics constraints of the plant are transformed into a general multi-chained form, and a desired velocity input function is designed by utilizing backstepping control technique. In the second stage, the proposed controller is designed by using variable structure control (VSC) methodology with adaptive mechanism embedded, so that the tracking errors of both transformed states and the original states are able to achieve asymptotic stability. In addition, the velocity trajectories of the controlled systems can track the desired velocity input function designed in the first stage in a finite time. The upper bounds of perturbations are not required to be known in advance due to employed adaptive mechanisms. Finally, a practical example is given for demonstrating the feasibility of the proposed control scheme.