Robust adaptive control of a class of nonlinear mechanical systems with unbounded and fast-varying uncertainties

Abstract

The class of system addressed in this paper consists of multibody mechanisms with open or closed kinematic chains. The constraints imposed by interbody connections are holonomic and scleronomic. Uncertainties result from unknown system parameters, external disturbances and some unmodeled dynamic effects. The plant model, available for a controller, represents only a few very general properties of multibody dynamic systems. The coefficients and terms of the plant equation may be potentially unbounded and fast varying. Such a general model includes a large class of unmodeled dynamics and any bounded external disturbances. Novel adaptive and control laws are presented. The stability and robustness analysis, performed by the Lyapunov method, has proven that the proposed controller keeps the tracking errors within a certain computable tolerance. As a particular case of the general theory, the tracking control of robotic manipulators has been discussed in detail.