scholarly journals L. S. Pontryagin maximum principle for some optimal control problems by trajectories pencils

2018 ◽  
Vol 14 (1) ◽  
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Pontryagin Maximum Principle ◽  
Optimal Control Problems ◽  
Control Problems

scholarly journals A Pontryagin Maximum Principle in Wasserstein spaces for constrained optimal control problems

2019 ◽  
Vol 25 ◽  
pp. 52 ◽  
Author(s):  
Benoît Bonnet
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Pontryagin Maximum Principle ◽  
Optimal Control Problems ◽  
Classical Method ◽  
Control Problems ◽  
Constrained Optimal Control ◽  
Non Local ◽  
Wasserstein Space ◽  
Needle Variations

In this paper, we prove a Pontryagin Maximum Principle for constrained optimal control problems in the Wasserstein space of probability measures. The dynamics is described by a transport equation with non-local velocities which are affine in the control, and is subject to end-point and running state constraints. Building on our previous work, we combine the classical method of needle-variations from geometric control theory and the metric differential structure of the Wasserstein spaces to obtain a maximum principle formulated in the so-called Gamkrelidze form.

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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