Design of robust adaptive variable structure tracking controllers with application to rigid robot manipulators

Based on the Lyapunov stability theorem, a variable structure control (VSC) scheme with adaptive mechanisms embedded is proposed in this study for a class of perturbed multi-input multi-output (MIMO) non-linear systems to solve robust tracking problems. The dynamic equation of the control system contains a perturbed leading coefficient matrix, which can be either positive definite or negative definite, and the perturbation is composed of parameter variations, input gain uncertainties, external disturbances etc. By introducing some adaptive mechanisms embedded in the variable structure controller, the proposed control scheme is capable of suppressing the perturbations to achieve asymptotic stability without knowing their upper bounds except for those of the uncertainties of the input gains. An example of its application to a rigid robot manipulator is included.