A Survey on Regularity Conditions for State-Constrained Optimal Control Problems and the Non-degenerate Maximum Principle

2019 ◽  
Vol 184 (3) ◽  
pp. 697-723 ◽  
Author(s):  
Aram Arutyunov ◽  
Dmitry Karamzin
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problems ◽  
Regularity Conditions ◽  
Control Problems ◽  
Constrained Optimal Control

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 Nonlinearly constrained optimal control problems

1992 ◽  
Vol 33 (4) ◽  
pp. 517-530 ◽  
Author(s):  
K. L. Teo ◽  
K. H. Wong
Keyword(s):  
Optimal Control ◽  
General Class ◽  
State Constraints ◽  
Computational Algorithm ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Constrained Optimal Control ◽  
Continuous State ◽  
Constraint Transcription ◽  
Inequality Type

AbstractIn a paper by Teo and Jennings, a constraint transcription is used together with the concept of control parametrisation to devise a computational algorithm for solving a class of optimal control problems involving terminal and continuous state constraints of inequality type. The aim of this paper is to extend the results to a more general class of constrained optimal control problems, where the problem is also subject to terminal equality state constraints. For illustration, a numerical example is included.

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