A nonlinear universal servomechanism

A servomechanism problem of controlling a scalar output variable to λ-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 “λ-tracking” is used in the following sense: for arbitrary prescribed λ>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 [-λ,λ]⊂ R. The instantaneous values of the reference signal and scaler output only are available for feedback. Adopting the space W^1,∞(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