Self-adjusting leakage type adaptive robust control design for uncertain systems with unknown bound

Abstract

Abstract The control problem for an uncertain mechanical system is addressed. The mechanical system under consideration, which is to follow a class of prescribed constraints, contains (possibly fast) time-varying uncertainty. The uncertainty is bounded, but the bound is not necessarily known. A new class of robust control schemes is proposed, which is based on on-line adaptation of a design parameter. Two categories of adaptation laws, both are based on self-adjusting leakage, are proposed. The control guarantees uniform boundedness and uniform ultimate boundedness of a performance measure. Comparing with the previous control scheme, the importance of this new control is that it can compensate the uncertainty in a very effective way. It also avoids over compensation and renders modest control effort. For demonstration purpose, the Toda Lattice, an ideal model of mechanical system with asymmetrical behaviour is chosen. The energy control of the Toda Lattice demonstrates the validity and reliability of control schemes and adaptation laws.