Robust global asymptotic continuous stabilisers for imperfectly known systems with stable drift subsystems

Abstract

A class of robust stabilising controls is synthesised for a class of imperfectly known dynamical systems. The uncertain systems are modelled as perturbations to a known composite prototype system, which consists of two nonlinearly coupled subsystems. Each perturbed subsystem contains both matched and residual uncertainty, which can be dependent on the states of the subsystem and any inputs to that subsystem. It is assumed that a drift system, associated with a particular subsystem of the prototype system, has a stable, but not necessarily asymptotically stable, equilibrium point. Such a prototype system can give rise to chaotic dynamics and the control of such systems is important. The design of the controllers is based on deterministic control methodology which does not require full identification of the uncertain elements. Only a knowledge of structural properties and bounds relating to the uncertainty is required. The design of the feedbacks is such that the controls are continuous everywhere. For each uncertain system the continuous feedbacks guarantee global asymptotic stability of the zero state.