An adaptive output feedback control for a class of nonlinear systems with time-varying parameters

We consider a class of observable, minimum phase single-input, single-output nonlinear systems evolving in Rⁿ with relative degree ρ and p uncertain differentiable time varying parameters θ(t), belonging to a known compact set Ω⊂R^p, whose time derivatives θ˙(t) are bounded, but are not restricted to be small or to have known bounds. We design a dynamic output feedback controller such that, for any initial condition: 1) all signals are bounded; 2) the effects of parameter uncertainties on the tracking error are arbitrarily attenuated; and 3) when θ˙(t)∈L₁, asymptotic tracking is guaranteed with arbitrarily good transient performance. Adaptation may be switched off at any time, still retaining the closed-loop properties 1) and 2)