Regulation of Continuous-Time Linear Input Delayed Systems Without Delay Knowledge

Abstract

In this chapter, we propose a control scheme that, in the absence of any knowledge of the delay, regulates to zero the state and the control input of a linear input delayed system whose open loop poles are at the origin or in the open left-half plane. 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, neither its exact value nor its upper bound , is required. The main ingredients of our control scheme and the regulation proof include the design of a delay independent truncated predictor feedback law with a time-varying feedback parameter , 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 of the closed-loop system.