UGAS and ULES of nonautonomous systems: Applications to integral control of ships and manipulators

Abstract

Nonlinear, adaptive backstepping design is applied to the tracking control problem for a class of strictly passive time-varying systems. The main contribution of this paper is to show that the (time-varying) closed-loop tracking error system has an equilibrium, corresponding to zero steady-state tracking error, that is uniformly globally asymptotically stable (UGAS) and uniformly locally exponentially stable (ULES). These properties (and a uniform local Lip-schitz condition) guarantee robustness of stability while weaker properties, like uniform global stability plus global convergence, do not. We show an application of our results, to the tracking control of robot manipulators and marine vessels, affected by constant disturbances. The result for these applications is UGAS and ULES of the closed loop, while rejecting the disturbances via an integral action.