On switching properties of time optimal controls for linear ODEs

Shulin Qin; Gengsheng Wang; Huaiqiang Yu

doi:10.3934/mcrf.2020039

Article Contents

2021, Volume 11, Issue 2: 329-351. Doi: 10.3934/mcrf.2020039

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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
^* Corresponding author: Huaiqiang Yu

Received: October 31, 2019

Revised: May 31, 2020

Early access: October 2020

Published: June 2021

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

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Abstract

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.

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Mathematics Subject Classification: Primary: 93C15; Secondary: 49J15.

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References

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