Adaptive output feedback tracking for nonlinear systems with time-varying parameters

Abstract

We consider a class of single-input, single-output nonlinear systems with uncertain differentiable time varying parameters /spl theta/(t)=(/spl theta//sub 1/(t),...,/spl theta//sub p/(t)) belonging to a known compact set whose time-derivative /spl theta//spl dot/(t) is not restricted to be small or to have known bounds. In particular, the assumption of slowly time-varying parameters, which is always made in the linear adaptive literature, is not required here. Given a smooth bounded reference signal y/sub r/(t) for the output y, we design an adaptive output feedback control algorithm such that for any initial condition all signals are bounded, when /spl theta//spl dot/(t)=/spl ne/0, i.e. /spl theta/(t) is constant, asymptotic tracking is guaranteed with arbitrarily good transient performance in terms of both L/sub 2/ and L/sub /spl infin// tracking error norms; and when /spl theta//spl dot/(t)/spl ne/0, the influence of the parameter estimation error and parameter time derivatives on the tracking error is arbitrarily attenuated.