A nonlinear universal servomechanism

Abstract

A servomechanism problem of controlling a scalar output variable to /spl lambda/-track any reference signal from some prescribed function space R, whilst maintaining internal states bounded, is addressed for a class S of uncertain nonlinearly-perturbed, single-input, single-output, minimum-phase, relative-degree-one, linear systems with nonlinear actuator characteristics (encompassing, for example, hysteresis and dead-zone effects). The actuator characteristics are required only to be contained in the graph of a suitably regular set-valued map. The terminology "/spl lambda/-tracking" is used in the following sense: for arbitrary prescribed /spl lambda/>0, an (adaptive) feedback strategy is sought which, for every reference signal of class R and every system (unknown to the controller) of class S, ensures that the tracking error is asymptotic to the interval /spl lsqb//spl minus//spl lambda/,/spl lambda//spl rsqb//spl sub/R. The instantaneous values of the reference signal and scaler output only are available for feedback. Adopting the space W/sup 1,/spl infin//(R) as the set R of admissible reference signals and under fairly weak assumptions on the nature of the system nonlinearities, one such (R, S)-universal adaptive feedback solution to this servomechanism problem is constructed. The feedback is continuous and its construction does not invoke an internal model principle.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>