Pontryagin Maximum Principle for Distributed-Order Fractional Systems
Keyword(s):
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.
A new approach to the Pontryagin maximum principle for nonlinear fractional optimal control problems
2016 ◽
Vol 39
(13)
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pp. 3640-3649
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On the formulation and numerical simulation of distributed-order fractional optimal control problems
2017 ◽
Vol 52
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pp. 177-189
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2019 ◽
Vol 351
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pp. 344-363
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2016 ◽
Vol 45
(1)
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pp. 59-74
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2017 ◽
Vol 40
(6)
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pp. 2054-2061
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2019 ◽
Vol 362
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pp. 124563
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