scholarly journals The Pontryagin maximum principle for solving Fokker–Planck optimal control problems

2020 ◽  
Vol 76 (2) ◽  
pp. 499-533 ◽  
Author(s):  
Tim Breitenbach ◽  
Alfio Borzì
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Pontryagin Maximum Principle ◽  
Optimal Control Problems ◽  
Control Problems ◽  
The Pontryagin Maximum Principle ◽  
Fokker Planck

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 First order necessary optimal conditions in Gursat-Darboux stochastic systems

2021 ◽  
Vol 21 (1) ◽  
pp. 89-104
Author(s):  
R.O. Mastaliyev ◽  
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Stochastic Systems ◽  
Optimal Control Problems ◽  
Necessary Optimality Conditions ◽  
Control Problems ◽  
Optimal Conditions ◽  
First Order ◽  
System A ◽  
The Pontryagin Maximum Principle

For optimal control problems, described by the Gursat-Darboux stochastic system, a number of first-order necessary optimality conditions are formulated and proved, which are the stochastic analogue - the Pontryagin maximum principle, the linearized maximum principle and the Euler equation.

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