Adaptive variable structure control of a class of nonlinear systems with nonvanishing perturbations via backstepping

Adaptive variable structure control of a class of nonlinear systems is considered in this paper. The advocated design technique is an improvement over our earlier work on robust control of nonlinear systems. The (parametric and dynamic) uncertainties are assumed to be bounded by polynomial type bounds in the states, with a constant bounding term present for the subsystem matched with the actual control input. It is shown that global asymptotic regulation may be achieved using the advocated control law. The improvement is due to a smooth sliding mode-type control action.