Optimal Error Quantification and Robust Tracking under Unknown Upper Bounds on Uncertainties and Biased External Disturbance

Abstract

This paper addresses a problem of optimal error quantification in the framework of robust control theory in the 𝓁1 setup. The upper bounds of biased external disturbance and the gains of coprime factor perturbations in a discrete-time linear time invariant SISO plant are assumed to be unknown. The computation of optimal data-consistent upper bounds under a known bias of external disturbance has been simplified to linear programming. This allows for the computation of optimal estimates in real-time and their application to achieve optimal robust steady-state tracking even when facing an unknown bias in the external disturbance. The presented results have been illustrated through computer simulations.