On the Dead-Time Compensation from<tex>$L^1$</tex>Perspectives

Abstract

Abstract-It is known that both H 2 and H 1 optimization problems for dead-time systems are solved by controllers having the so-called modified Smith predictor (dead-time compensator) structure. This note shows that this is also true for the L 1 control problem. More precisely, it is demonstrated that the use of the modified Smith predictor enables one to reduce the standard L 1 problem for systems with a single loop delay to an equivalent delay-free problem. The (sub)optimal solution therefore always contains the modified Smith predictor.

Optimal coordination of homogeneous agents subject to delayed information exchange

“…This implementation contains two infinite-dimensional dynamical elements: the pure delay e sh , which is easy to implement, and the distributed-delay system˘. The latter is an intrinsic part of many optimal control strategies, see, e.g., [14]- [18], which study problems with a single delay.…”

New results on robust exponential stability of integral delay systems

“…(2) Feedback schemes involving delay compensation as the finite spectrum assignment (FSA) (Manitius & Olbrot, 1979), stabilisation problems (Mayne, 1968;Watanabe & Ito, 1981) and optimal control (Meinsma & Zwart, 2000;Mirkin, 2006;Tadmord, 2000) of systems with time delay. In these problems, the compensators necessarily include an infinite-dimensional dynamic governed by an integral delay system.…”