Impulse and sampled-data optimal control of heat equations, and error estimates - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue SIAM Journal on Control and Optimization Année : 2016

Impulse and sampled-data optimal control of heat equations, and error estimates

Emmanuel Trélat
Lijuan Wang
  • Fonction : Auteur
  • PersonId : 943728
Yubiao Zhang
  • Fonction : Auteur
  • PersonId : 970425

Résumé

We consider the optimal control problem of minimizing some quadratic functional over all possible solutions of an internally controlled multi-dimensional heat equation with a periodic terminal state constraint. This problem has a unique optimal solution, which can be characterized by an optimality system derived from the Pontryagin maximum principle. We define two approximations of this optimal control problem. The first one is an impulse approximation, and consists of considering a system of linear heat equations with impulse control. The second one is obtained by the sample-and-hold procedure applied to the control, resulting into a sampled-data approximation of the controlled heat equation. We prove that both problems have a unique optimal solution, and we establish precise error estimates for the optimal controls and optimal states of the initial problem with respect to its impulse and sampled-data approximations.
Fichier principal
Vignette du fichier
Error-estimate.pdf (368.58 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01202251 , version 1 (19-09-2015)

Identifiants

Citer

Emmanuel Trélat, Lijuan Wang, Yubiao Zhang. Impulse and sampled-data optimal control of heat equations, and error estimates. SIAM Journal on Control and Optimization, 2016, 54 (5), pp.2787--2819. ⟨hal-01202251⟩
298 Consultations
101 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More