Switching properties of time optimal controls for systems of heat equations coupled by constant matrices

TL;DR

This paper investigates the structure of time optimal controls for coupled heat equations, establishing bounds on switching points and characterizing control jumps at these points.

Contribution

It provides new bounds on the number of switching points and describes the control behavior at switching times for coupled heat equation systems.

Findings

Upper bound for switching points in each interval

Control jumps from one direction to the reverse at switching points

Characterization of control behavior at switching points

Abstract

This paper studies the time optimal control problem for systems of heat equations coupled by a pair of constant matrices. The control constraint is of the ball-type, while the target is the origin of the state space. We obtain an upper bound for the number of switching points of the optimal control over each interval with a fixed length. Also, we prove that at each switching point, the optimal control jump from one direction to the reverse direction.