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

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2017
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Kamoutsi, Angeliki
Mohajerin Esfahani, Peyman
Lygeros, John
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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.

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Optimal control, discounted occupation measures, moments, sum-of-squares, infinite linear programming
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ISO 690KAMOUTSI, 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), pp. 134-139. eISSN 2475-1456. Available under: 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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