Equivalence of three different kinds of optimal control problems for heat equations and its applications

TL;DR

This paper proves an equivalence theorem linking three types of optimal control problems for heat equations and develops algorithms for optimal norm and time controls based on this theorem.

Contribution

It introduces a novel equivalence theorem connecting different optimal control problems for heat equations and provides algorithms for computing optimal controls.

Findings

Established an equivalence theorem for three control problem types.

Developed algorithms for optimal norm and time controls.

Constructed a feedback law for optimal norms.

Abstract

This paper presents an equivalence theorem for three different kinds of optimal control problems, which are optimal target control problems, optimal norm control problems and optimal time control problems. Controlled systems in this study are internally controlled heat equations. With the aid of this theorem, we establish an optimal norm feedback law and build up two algorithms for optimal norms (together with optimal norm controls) and optimal time (along with optimal time controls), respectively.