Geodesic
Homotopic approach for turnpike and singularly perturbed optimal control problems
Olivier Cots1 ; Joseph Gergaud1 ; Boris Wembe2
1Toulouse Univ., INP-ENSEEIHT-IRIT, UMR CNRS 5505, 2 rue Camichel, 31071 Toulouse, France
2Toulouse Univ., IRIT-UPS, UMR CNRS 5505, 118 route de Narbonne, 31062 Toulouse, France
ESAIM. Proceedings, Tome 71 (2021), pp. 43-53
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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.
DOI : 10.1051/proc/202171105

Olivier Cots  1   ; Joseph Gergaud  1   ; Boris Wembe  2

1 Toulouse Univ., INP-ENSEEIHT-IRIT, UMR CNRS 5505, 2 rue Camichel, 31071 Toulouse, France
2 Toulouse Univ., IRIT-UPS, UMR CNRS 5505, 118 route de Narbonne, 31062 Toulouse, France 
@article{EP_2021_71_a5,
     author = {Olivier Cots and Joseph Gergaud and Boris Wembe},
     title = {Homotopic approach for turnpike and singularly perturbed optimal control problems},
     journal = {ESAIM. Proceedings},
     pages = {43--53},
     year = {2021},
     volume = {71},
     doi = {10.1051/proc/202171105},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/202171105/}
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Olivier Cots; Joseph Gergaud; Boris Wembe. Homotopic approach for turnpike and singularly perturbed optimal control problems. ESAIM. Proceedings, Tome 71 (2021), pp. 43-53. doi: 10.1051/proc/202171105

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