On Infinite Linear Programming and the Moment Approach to Deterministic Infinite Horizon Discounted Optimal Control Problems

Kamoutsi, Angeliki; Sutter, Tobias; Mohajerin Esfahani, Peyman; Lygeros, John

On Infinite Linear Programming and the Moment Approach to Deterministic Infinite Horizon Discounted Optimal Control Problems

Dateien

Kamoutsi_2-uemss4neqlzm5.pdfGröße: 346.19 KBDownloads: 2

Datum

2017

Autor:innen

Kamoutsi, Angeliki

Sutter, Tobias

Mohajerin Esfahani, Peyman

Lygeros, John

Open Access-Veröffentlichung

Open Access Green

Sammlungen

Informatik und Informationswissenschaft

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

IEEE Control Systems Letters. IEEE. 2017, 1(1), S. 134-139. eISSN 2475-1456. Verfügbar unter: doi: 10.1109/LCSYS.2017.2710234

Zusammenfassung

We revisit the linear programming approach to deterministic, continuous time, infinite horizon discounted optimal control problems. In the first part, we relax the original problem to an infinite-dimensional linear program over a measure space and prove equivalence of the two formulations under mild assumptions, significantly weaker than those found in the literature until now. The proof is based on duality theory and mollification techniques for constructing approximate smooth subsolutions to the associated Hamilton-Jacobi-Bellman equation. In the second part, we assume polynomial data and use Lasserre's hierarchy of primal-dual moment-sum-of-squares semidefinite relaxations to approximate the value function and design an approximate optimal feedback controller. We conclude with an illustrative example.

Fachgebiet (DDC)

004 Informatik

Schlagwörter

Optimal control, discounted occupation measures, moments, sum-of-squares, infinite linear programming

Zitieren

ISO 690

KAMOUTSI, Angeliki, Tobias SUTTER, Peyman MOHAJERIN ESFAHANI, John LYGEROS, 2017. On Infinite Linear Programming and the Moment Approach to Deterministic Infinite Horizon Discounted Optimal Control Problems. In: IEEE Control Systems Letters. IEEE. 2017, 1(1), S. 134-139. eISSN 2475-1456. Verfügbar unter: doi: 10.1109/LCSYS.2017.2710234

BibTex

@article{Kamoutsi2017Infin-55612,
  year={2017},
  doi={10.1109/LCSYS.2017.2710234},
  title={On Infinite Linear Programming and the Moment Approach to Deterministic Infinite Horizon Discounted Optimal Control Problems},
  number={1},
  volume={1},
  journal={IEEE Control Systems Letters},
  pages={134--139},
  author={Kamoutsi, Angeliki and Sutter, Tobias and Mohajerin Esfahani, Peyman and Lygeros, John}
}

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