Format:
Online-Ressource
ISBN:
9783642110429
Series Statement:
C.I.M.E. Summer Schools 39
Content:
A. Blaquiere: Quelques aspects geometriques des processus optimaux.- C. Castaing: Quelques problemes de mesurabilite lies a la theorie des commandes.- L. Cesari: Existence theorems for Lagrange and Pontryagin problems of the calculus of variations and optimal control of more-dimensional extensions in Sobolev space.- H. Halkin: Optimal control as programming in infinite dimensional spaces.- C. Olech: The range of integrals of a certain class vector-valued functions.- E. Rothe: Weak topology and calculus of variations.- E.O. Roxin: Problems about the set of attainability
Note:
Description based upon print version of record
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Calculus of Variations, Classical and Modern; Copyright Page; Contents; Quelques Aspects Geometriques Des Processus Optimaux; I Definition Des Surfaces Limits, Proprietes Globales De Ces Surfaces; II Proprietes Locales Des Surfaces Limites; III Exemples Illustrant La Theorie; Quelques Problemes De Mesurabilite Lies a La Theorie Des Commandes; Existence Theorems for Langrange and Pontryagin Problems of The Calculus of Variations and Optimal Control. More Dimensional Extensions In Sobolev Spaces; Lecture 1. Usual and generalized solutions in Optimal control and the calculus of variations
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Lecture 2. Upper semicontinuity of variable sets generalizationsLecture 3. Closure Theorems; Lecture 4. Existence theorems for usual solutions of Langrage problems; Lecture 5. Existence theorems for generalized solutions of Langrange problems; Lecture 6. A system of partial differential equations in Sobolev spaces; Lecture 7. A closure theorem in Sobolev spaces; Lecture 8. Existence theorems for Pontryagin's problems in Sobolev speces; References; Optimal Control as Programming In Infinite Dimensional Spaces; Introduction; References
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The range of integrals of a certain class of vector-valued functionsIntroduction; References; Weak Topology and Calculus of Variations; 1. Introduction; 2. General theorems on lower semi-continuous and on convex functions; 3. Weak topology in Banach spaces; 4. On the existence of extrema; 5. On the relation between f and its Gâteaux differential (Image); 6. Applications to Sobolev spaces; Bibliography; Problems About the Set of Attainability; I. Control systems. Attainable set; II. Properties of the attainable set; III. Control systems defined abstractly
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IV. Control systems and calculus of variationsV. Boundary controls; VI. Controllability of linear systems; VII. Controllability of nonlinear systems; VIII. Singular problems. Not controllable systems; References;
Language:
English
Keywords:
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