A universal servomechanism for a class of nonlinear planar systems

摘要

A servomechanism problem of controlling a scalar output variable to track any given reference signal of Sobolev class W3,∞(R) ≕ R, while maintaining state boundedness, is addressed for a class Sδ of uncertain, single-input, single-output, nonlinear planar systems (encompassing, for example, various uncertain, single-degree-of-freedom, mechanical models with extraneous disturbances and a damping effect quantified by the parameter δ, and with position y(t), but not velocity ẏ(t), available for feedback). The instantaneous values of the reference signal and scalar output only are available for feedback. An (R, Sδ)-universal servomechanism is presented. Specifically, an adaptive discontinuous feedback control is constructed which is (R, Sδ) universal in the sense that, for any given reference signal of class R and every system (unknown to the controller) of class Sδ, the strategy ensures that the tracking error is asymptotic to zero.