Necessary optimality conditions for two-step descriptor systems

Xin Wang; Yuxiang Liu; Lisha Wang; Xin Wang; Yuxiang Liu; Lisha Wang

doi:10.3934/math.2022503

AIMS Mathematics

2022, Volume 7, Issue 5: 9039-9056. doi: 10.3934/math.2022503

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Research article

Necessary optimality conditions for two-step descriptor systems

School of Science, Qingdao University of Technology, Qingdao, Shandong 266400, China

Received: 26 October 2021 Revised: 28 February 2022 Accepted: 01 March 2022 Published: 08 March 2022
MSC : 34A38, 90C46, 35A15, 80M30

This paper is concerned with an optimal control problem for general two-step descriptor systems. Based on the nonsmooth analysis and variational techniques, we establish the first-order necessary optimality conditions. Then, due to the expression of the general solution for linear descriptor systems, which is established by virtue of the Drazin inverse, we derived the generalized second-order necessary conditions for the first time. Also, for unfixed switching point case, we give some discussions.
- steps descriptor systems,
- nonsmooth analysis,
- necessary optimality conditions,
- variational techniques
Citation: Xin Wang, Yuxiang Liu, Lisha Wang. Necessary optimality conditions for two-step descriptor systems[J]. AIMS Mathematics, 2022, 7(5): 9039-9056. doi: 10.3934/math.2022503

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Abstract

This paper is concerned with an optimal control problem for general two-step descriptor systems. Based on the nonsmooth analysis and variational techniques, we establish the first-order necessary optimality conditions. Then, due to the expression of the general solution for linear descriptor systems, which is established by virtue of the Drazin inverse, we derived the generalized second-order necessary conditions for the first time. Also, for unfixed switching point case, we give some discussions.

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