Adaptive Regulation of a Chain of Integrators under Unknown and Time-Varying Individual State Delays

Abstract

In this letter, we study the adaptive regulation problem for a chain of integrators in which there are different individual delays in measured feedback states for a controller. These delays are considered to be unknown and time-varying, and they can be arbitrarily fast-varying. We analytically show that a feedback controller with a dynamic gain can adaptively regulate a chain of integrators in the presence of unknown individual state delays. A simulation result is given for illustration.