Optimal Control Problems Governed by Fractional Differential Equations with Control Constraints
Abstract
A class of optimal control problems governed by fractional differential equations with control constraints and free right end point is considered. We first prove a result on the existence of optimal solutions for the case where the state equation may be nonlinear in control variable. Then we establish first- and second-order optimality conditions for locally optimal solutions to the general problem. When $\frac{1}2<\alpha<1$, a theory of no-gap second-order conditions is obtained. A result on regularity of optimal solution for the case where the state equation is linear in control variable is also given.
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Published In
SIAM Journal on Control and Optimization
Pages: 1732 - 1762
DOI: 10.1137/21M1430728
ISSN (online): 1095-7138
Copyright
© 2022, Society for Industrial and Applied Mathematics.
History
Submitted: 1 July 2021
Accepted: 7 March 2022
Published online: 14 June 2022
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Funding Information
Russian Foundation for Basic Research https://doi.org/10.13039/501100002261 : 21-51-54003
Funding Information
Vietnam Academy of Science and Technology https://doi.org/10.13039/100012046 : QTRU 01-01/21-22
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