Optimal control of infinite dimensional bilinear systems: Application to the heat and wave equations

TL;DR

This paper develops second order optimality conditions for bilinear control problems governed by infinite-dimensional systems, specifically applying the results to heat and wave equations using the Goh transform.

Contribution

It introduces new second order optimality conditions for infinite-dimensional bilinear systems and demonstrates their application to heat and wave equations.

Findings

Derived first and second order optimality conditions using the Goh transform.

Applied the theoretical results to control problems for heat and wave equations.

Provided a framework for analyzing bilinear control systems in infinite dimensions.

Abstract

In this paper we consider second order optimality conditions for a bilinear optimal control problem governed by a strongly continuous semigroup operator, the control entering linearly in the cost function. We derive first and second order optimality conditions, taking advantage of the Goh transform. We then apply the results to the heat and wave equations.