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Research Article | Open Access

Necessary optimality conditions for two-step descriptor systems

Xin Wang( ), Yuxiang Liu, Lisha Wang
School of Science, Qingdao University of Technology, Qingdao, Shandong 266400, China
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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.

Keywords

steps descriptor systemsnonsmooth analysisnecessary optimality conditionsvariational techniques
CLC number: 34A38, 90C46, 35A15, 80M30

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AIMS Mathematics
Volume 7 Issue 5,
May 2022
Pages 9039-9056
DOI: 10.3934/math.2022503

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Cite this article:
Wang X, Liu Y, Wang L. Necessary optimality conditions for two-step descriptor systems. AIMS Mathematics, 2022, 7(5): 9039-9056. https://doi.org/10.3934/math.2022503

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Received: 26 October 2021
Revised: 28 February 2022
Accepted: 01 March 2022
Published: 15 May 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)