Pontryagin Maximum Principle for Distributed-Order Fractional Systems

We consider distributed-order non-local fractional optimal control problems with controls taking values on a closed set and prove a strong necessary optimality condition of Pontryagin type. The possibility that admissible controls are subject to pointwise constraints is new and requires more sophist...

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Published inMathematics (Basel) Vol. 9; no. 16; p. 1883
Main Authors Ndaïrou, Faïçal, Torres, Delfim F. M.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 02.08.2021
Subjects
Calculus
Composite materials
distributed-order fractional calculus
Mathematics
Maximum principle
needle-like variations
Optimal control
Optimization
Perturbation
Pontryagin maximum principle
Viscoelasticity
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Summary:We consider distributed-order non-local fractional optimal control problems with controls taking values on a closed set and prove a strong necessary optimality condition of Pontryagin type. The possibility that admissible controls are subject to pointwise constraints is new and requires more sophisticated techniques to include a maximality condition. We start by proving results on continuity of solutions due to needle-like control perturbations. Then, we derive a differentiability result on the state solutions with respect to the perturbed trajectories. We end by stating and proving the Pontryagin maximum principle for distributed-order fractional optimal control problems, illustrating its applicability with an example.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math9161883