Regulation of Linear Input Delayed Systems in the Absence of Delay Knowledge

Abstract

In this paper, we propose a delay independent control scheme that regulates to zero the state and the control input of a linear input delayed system whose open loop poles are at the origin. Two main features of our control scheme are its non-distributed nature in the sense that only the current state is used in the feedback, and its delay independence in the sense that no knowledge of the delay is required. The main ingredients of our control scheme and the regulation proof include a design of the delay independent truncated predictor feedback law with a time-varying feedback parameter, a Lyapunov function based adaptation of the time-varying parameter, a mechanism for switching between two update laws of the time-varying parameter, and the partial differential equation based analysis for delayed systems.