Adaptive suboptimal tracking under bounded Lipshitz uncertainty in a discrete minimum-phase object

Abstract

We consider a deterministic problem of asymptotically suboptimal tracking of a bounded reference signal with the output of a scalar discrete minimum-phase object with unknown transition function under a bounded external disturbance and bounded nonlinear stationary uncertainty satisfying a generalized Lipschitz condition. Suboptimality of the tracking is achieved with online estimation and compensation for nonparametric Lipschitz uncertainty in addition to estimating an unknown transition function. To solve the problem we use two parallel estimation algorithms, one of which provides stability for the closed adaptive system, the other, asymptotic tracking optimality with desired accuracy.