Type(s) de contenu et mode(s) de consultation : Texte noté : électronique

Auteur(s) : Fattorini, Hector O. (1938-....)  Voir les notices liées en tant qu'auteur

Titre(s) : Infinite dimensional linear control systems [Texte électronique] : the time optimal and norm optimal problems / H.O. Fattorini

Édition : 1st ed.

Publication : Amsterdam ; Boston : Elsevier, 2005

Description matérielle : 1 ressource dématérialisée

Collection : North-Holland mathematics studies ; 201

Note(s) : Includes bibliographical references (pages 309-318) and index
For more than forty years, the equation y'(t) = Ay(t) + u(t) in Banach spaces has been used as model for optimal control processes described by partial differential equations, in particular heat and diffusion processes. Many of the outstanding open problems, however, have remained open until recently, and some have never been solved. This book is a survey of all results know to the author, with emphasis on very recent results (1999 to date). The book is restricted to linear equations and two particular problems (the time optimal problem, the norm optimal problem) which results in a more focused and concrete treatment. As experience shows, results on linear equations are the basis for the treatment of their semilinear counterparts, and techniques for the time and norm optimal problems can often be generalized to more general cost functionals. The main object of this book is to be a state-of-the-art monograph on the theory of the time and norm optimal controls for y'(t) = Ay(t) + u(t) that ends at the very latest frontier of research, with open problems and indications for future research

Sujet(s) : Théorie de la commande  Voir les notices liées en tant que sujet
Optimisation mathématique  Voir les notices liées en tant que sujet
Commande linéaire  Voir les notices liées en tant que sujet
Calcul des variations  Voir les notices liées en tant que sujet

Indice(s) Dewey :  629.8 (23e éd.) = Technique de la commande automatique  Voir les notices liées en tant que sujet

Identifiants, prix et caractéristiques : ISBN 9780444516329

Identifiant de la notice  : ark:/12148/cb446465670

Notice n° :  FRBNF44646567 (notice reprise d'un réservoir extérieur)

Table des matières : 1: INTRODUCTION: 1.1 Finite dimensional systems: the maximum principle ; 1.2. Finite dimensional systems: existence and uniqueness ; 1.3. Infinite dimensional systems ; 2: SYSTEMS WITH STRONGLY MEASURABLE CONTROLS, I ; 2.1. The reachable space and the bang-bang property ; 2.2. Reversible systems ; 2.3. The reachable space and its dual, I ; 2.4. The reachable space and its dual, II ; 2.5. The maximum principle ; 2.6. Vanishing of the costate and nonuniqueness for norm optimal controls ; 2.7. Vanishing of the costate for time optimal controls ; 2.8. Singular norm optimal controls ; 2.9. Singular norm optimal controls and singular functionals ; 3: SYSTEMS WITH STRONGLY MEASURABLE CONTROLS, II: 3.1. Existence and uniqueness of optimal controls ; 3.2. The weak maximum principle and the time optimal problem ; 3.3. Modeling of parabolic equations ; 3.4. Weakly singular extremals ; 3.5. More on the weak maximum principle ; 3.6. Convergence of minimizing sequences and stabi