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

We consider a class of single-input, single-output nonlinear systems with uncertain differentiable time varying parameters θ(t)=(θ₁(t),...,θ_p(t)) belonging to a known compact set whose time-derivative θ˙(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_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 θ˙(t)=≠0, i.e. θ(t) is constant, asymptotic tracking is guaranteed with arbitrarily good transient performance in terms of both L₂ and L_∞ tracking error norms; and when θ˙(t)≠0, the influence of the parameter estimation error and parameter time derivatives on the tracking error is arbitrarily attenuated