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]
3 GIPSA-SYSCO - SYSCO
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.
Document type :
Journal articles
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-01966782
Contributor : Victor Magron <>
Submitted on : Saturday, December 29, 2018 - 5:02:57 PM
Last modification on : Friday, June 14, 2019 - 6:31:22 PM

Identifiers

Relations

Citation

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⟩

Share

Metrics

Record views

134