scholarly journals A new approach to the Pontryagin maximum principle for nonlinear fractional optimal control problems

2016 ◽  
Vol 39 (13) ◽  
pp. 3640-3649 ◽  
Author(s):  
Hegagi M. Ali ◽  
Fernando Lobo Pereira ◽  
Sílvio M. A. Gama
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Pontryagin Maximum Principle ◽  
Optimal Control Problems ◽  
Control Problems ◽  
New Approach ◽  
Fractional Optimal Control ◽  
Fractional Optimal Control Problems ◽  
The Pontryagin Maximum Principle

scholarly journals Pontryagin Maximum Principle for Distributed-Order Fractional Systems

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1883
Author(s):  
Faïçal Ndaïrou ◽  
Delfim F. M. Torres
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Pontryagin Maximum Principle ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Closed Set ◽  
Fractional Optimal Control ◽  
Fractional Optimal Control Problems ◽  
Pointwise Constraints ◽  
Distributed Order

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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