Optimal Control of Linear PDEs using Occupation Measures and SDP Relaxations

Victor Magron 1, 2 Christophe Prieur 3
2 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes [Toulouse]
GIPSA-DA - Département Automatique
Abstract : This paper addresses the problem of solving a class of optimal control problems (OCPs) with infinite-dimensional linear state constraints involving Riesz-spectral operators. Each instance within this class has time/control-dependent polynomial Lagrangian cost and control constraints described by polynomials. We first perform a state-mode discretization of the Riesz-spectral operator. Then we approximate the resulting finite-dimensional OCPs by using a previously known hierarchy of semidefinite relaxations. Under certain compactness assumptions, we provide a converging hierarchy of semidefinite programming relaxations whose optimal values yield lower bounds for the initial OCP. We illustrate our method by two numerical examples, involving a diffusion partial differential equation and a wave equation. We also report on the related experiments.
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Journal articles
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Submitted on : Saturday, December 29, 2018 - 5:02:57 PM
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Victor Magron, Christophe Prieur. Optimal Control of Linear PDEs using Occupation Measures and SDP Relaxations. IMA Journal of Mathematical Control and Information, Oxford University Press (OUP), 2018, ⟨10.1093/imamci/dny044⟩. ⟨hal-01966782⟩



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