# American Institute of Mathematical Sciences

doi: 10.3934/mcrf.2020039

## On switching properties of time optimal controls for linear ODEs

 1 School of Science, Tianjin University of Commerce, Tianjin, 300134, China 2 Center for Applied Mathematics, Tianjin University, Tianjin, 300072, China 3 School of Mathematics, Tianjin University, Tianjin, 300354, China

* Corresponding author: Huaiqiang Yu

Received  November 2019 Revised  June 2020 Published  October 2020

Fund Project: This work was partially supported by the NNSF of China under grants 11601377, 11901432, 11971022

In this paper, we present some properties of time optimal controls for linear ODEs with the ball-type control constraint. More precisely, given 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.

Citation: Shulin Qin, Gengsheng Wang, Huaiqiang Yu. On switching properties of time optimal controls for linear ODEs. Mathematical Control & Related Fields, doi: 10.3934/mcrf.2020039
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