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

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.