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July  2019, 15(3): 1399-1419. doi: 10.3934/jimo.2018101

## Necessary optimality conditions for nonautonomous optimal control problems and its applications to bilevel optimal control

 1 College of Mathematics and Informatics & FJKLMAA, Fujian Normal University, Fuzhou 350108, Fujian, China 2 School of Mathematical Sciences, Xiamen University, Xiamen 361005, Fujian, China

* Corresponding author. E-mail address: anlee@xmu.edu.cn

Received  October 2017 Revised  February 2018 Published  July 2018

Fund Project: The research was partially supported by Natural Science Foundation of China (Grant Nos. 11301081, 11671335), Natural Science Foundation of Fujian Province, China (Grant Nos. 2018J01657, 2016J01013) and Fundamental Research Funds for the Central Universities (Grant No. 20720160036).

This paper focuses on the development of necessary optimality conditions for nonautonomous optimal control problems with nonsmooth mixed state and control constraints. In most of the existing results, the necessary optimality conditions for nonautonomous optimal control problems with mixed state and control constraints are derived under the Mangasarian-Fromovitz condition or even stronger. In this paper we derive the necessary optimality conditions for nonautonomous optimal control problems under constraint qualifications which are weaker than Mangasarian-Fromovitz condition. Moreover necessary optimality conditions with an Euler inclusion taking a bounded explicit multiplier form are derived for certain cases. Specifying these results to bilevel optimal control problems with finite-dimensional lower level we obtain necessary optimality conditions under weaker qualification conditions.

Citation: Jianxiong Ye, An Li. Necessary optimality conditions for nonautonomous optimal control problems and its applications to bilevel optimal control. Journal of Industrial & Management Optimization, 2019, 15 (3) : 1399-1419. doi: 10.3934/jimo.2018101
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