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HJB EQUATIONS FOR THE OPTIMAL CONTROL OF DIFFERENTIAL EQUATIONS WITH DELAYS AND STATE CONSTRAINTS, II: VERIFICATION AND OPTIMAL FEEDBACKS

Identifieur interne : 006A60 ( Main/Exploration ); précédent : 006A59; suivant : 006A61

HJB EQUATIONS FOR THE OPTIMAL CONTROL OF DIFFERENTIAL EQUATIONS WITH DELAYS AND STATE CONSTRAINTS, II: VERIFICATION AND OPTIMAL FEEDBACKS

Auteurs : Salvatore Federico [France] ; Ben Goldys [Australie] ; Fausto Gozzi [Italie]

Source :

SIAM journal on control and optimization [ 0363-0129 ] ; 2011.

RBID : Pascal:14-0164034

Descripteurs français

Pascal (Inist)
- Commande optimale, Contrainte espace état, Rétroaction, Commande boucle fermée, Dimensionnalité, Etude économique, Croissance optimale, Temps exécution, Equation Hamilton Jacobi, Equation Bellman, Equation différentielle, Equation état, Equation à retard, Espace Hilbert, Régularité, Théorie preuve, Modèle non linéaire.

English descriptors

KwdEn :
- Bellman equation, Closed feedback, Delay equation, Differential equation, Dimensionality, Economic study, Equations of state, Execution time, Feedback regulation, Hamilton Jacobi equation, Hilbert space, Non linear model, Optimal control, Optimal growth, Proof theory, Regularity, State constraint.

Abstract

This paper, which is the natural continuation of part I [S. Federico, B. Goldys. and F. Gozzi, SIAM J. Control Optim., 48 (2010), pp. 4910-4937], studies a class of optimal control problems with state constraints where the state equation is a differential equation with delays. In part I the problem is embedded in a suitable Hilbert space H and the regularity of the associated Hamilton-Jacobi-Bellman equation is studied. The goal of the present paper is to exploit the regularity result of part 1 to prove a verification theorem and find optimal feedback controls for the problem. While it is easy to define a feedback control formally following the classical case, the proof of its existence and optimality is hard due to lack of full regularity of V and to the infinite dimensionality of the problem. The theory developed is applied to study economic problems of optimal growth for nonlinear time-to-build models. In particular, we show the existence and uniqueness of optimal controls and their characterization as feedbacks.

Affiliations:

Australie, France, Italie
Latium, Nouvelle-Galles du Sud, Toscane, Île-de-France
Paris, Pise, Rome, Sydney

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Le document en format XML

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HJB EQUATIONS FOR THE OPTIMAL CONTROL OF DIFFERENTIAL EQUATIONS WITH DELAYS AND STATE CONSTRAINTS, II: VERIFICATION AND OPTIMAL FEEDBACKS

HJB EQUATIONS FOR THE OPTIMAL CONTROL OF DIFFERENTIAL EQUATIONS WITH DELAYS AND STATE CONSTRAINTS, II: VERIFICATION AND OPTIMAL FEEDBACKS

Source :

Descripteurs français

English descriptors

Abstract

Links toward previous steps (curation, corpus...)

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri