On singular perturbations in optimal control problems

1986 ◽  
pp. 33-41
Author(s):  
S. G. Kreĭn ◽  
G. A. Kurina
Keyword(s):  
Optimal Control ◽  
Singular Perturbations ◽  
Optimal Control Problems ◽  
Control Problems

Singular perturbations in optimal control problems

1986 ◽  
Vol 34 (3) ◽  
pp. 1579-1629 ◽  
Author(s):  
A. B. Vasil'eva ◽  
M. G. Dmitriev
Keyword(s):  
Optimal Control ◽  
Singular Perturbations ◽  
Optimal Control Problems ◽  
Control Problems

scholarly journals Homotopic approach for turnpike and singularly perturbed optimal control problems

2021 ◽  
Vol 71 ◽  
pp. 43-53
Author(s):  
Olivier Cots ◽  
Joseph Gergaud ◽  
Boris Wembe
Keyword(s):  
Optimal Control ◽  
Singular Perturbations ◽  
Optimal Control Problems ◽  
Singularly Perturbed ◽  
Continuation Methods ◽  
Control Problems ◽  
General Control ◽  
Turnpike Property ◽  
Set Up ◽  
New Framework

The first aim of this article is to present the link between the turnpike property and the singular perturbations theory: the first one being a particular case of the second one. Then, thanks to this link, we set up a new framework based on continuation methods for the resolution of singularly perturbed optimal control problems. We consider first the turnpike case, then, we generalize the approach to general control problems with singular perturbations (that is with fast but also slow variables). We illustrate each step with an example.

On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Open Loop ◽  
Time Inconsistency ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

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