On switching properties of time optimal controls for linear ODEs

TL;DR

This paper investigates the switching behavior of time optimal controls in linear ODEs with control constraints, providing bounds on switching points, analyzing their directional changes, and describing their dynamics.

Contribution

It introduces bounds on the number of switching points and characterizes the switching directions and dynamics of optimal controls for linear ODEs.

Findings

Upper bound for number of switching points

Switching points involve direction reversal

Dynamic behavior between switches analyzed

Abstract

In this paper, we present some properties of time optimal controls for linear ODEs with the ball-type control constraint. More precisely, for an optimal control, we build up an upper bound for the number of its switching points; show that it jumps from one direction to the reverse direction at each switching point; give its dynamic behaviour between two consecutive switching points; and study its switching directions.