Infinite dimensional delay differential equations in control and sensitivity analysis

Abstract

In this paper we consider a specific class of infinite dimensional functional differential equations that are described by functional partial differential equations (FPDEs).  These FPDEs arise naturally in problems of control of systems governed by partial differential equations where delayed actuator dynamics are included and in the sensitivity analysis of such systems when one is concerned with sensitivities with respect to delays.   We present examples to motivate the models, establish the well-posedness for a class of FPDE systems in product spaces and use this formulation as a framework to develop efficient numerical approximations for control and simulation of the PDE problems. The theoretical results extend existing well-posedness results to problems where the standard range condition does not apply and we present a conjecture about a more general theorem. Finally, numerical results are given to illustrate the ideas.