Mathematical Methods in Optimization of Differential Systems by Viorel BarbuMathematical Methods in Optimization of Differential Systems by Viorel Barbu

Mathematical Methods in Optimization of Differential Systems

byViorel Barbu

Paperback | October 20, 2012

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This work is a revised and enlarged edition of a book with the same title published in Romanian by the Publishing House of the Romanian Academy in 1989. It grew out of lecture notes for a graduate course given by the author at the University if Ia<_i20_and20_was20_initially20_intended20_for20_students20_and20_readers20_primarily20_interested20_in20_applications20_of20_optimal20_control20_of20_ordinary20_differential20_equations.20_in20_this20_vision20_the20_book20_had20_to20_contain20_an20_elementary20_description20_of20_the20_pontryagin20_maximum20_principle20_and20_a20_large20_number20_of20_examples20_and20_applications20_from20_various20_fields20_of20_science.20_the20_evolution20_of20_control20_science20_in20_the20_last20_decades20_has20_shown20_that20_its20_methc2ad_20_ods20_and20_tools20_are20_drawn20_from20_a20_large20_spectrum20_of20_mathematical20_results20_which20_go20_beyond20_the20_classical20_theory20_of20_ordinary20_differential20_equations20_and20_real20_analyc2ad_20_ses.20_mathematical20_areas20_such20_as20_functional20_analysis2c_20_topology2c_20_partial20_differential20_equations20_and20_infinite20_dimensional20_dynamical20_systems2c_20_geometry2c_20_played20_and20_will20_continue20_to20_play20_an20_increasing20_role20_in20_the20_development20_of20_the20_control20_sciences.20_on20_the20_other20_hand2c_20_control20_problems20_is20_a20_rich20_source20_of20_deep20_mathematical20_problems.20_any20_presentation20_of20_control20_theory20_which20_for20_the20_sake20_of20_accessibility20_ignores20_these20_facts20_is20_incomplete20_and20_unable20_to20_attain20_its20_goals.20_this20_is20_the20_reason20_we20_considered20_necessary20_to20_widen20_the20_initial20_perspective20_of20_the20_book20_and20_to20_include20_a20_rigorous20_mathematical20_treatment20_of20_optimal20_control20_theory20_of20_processes20_governed20_by20_ordic2ad_20_nary20_differential20_equations20_and20_some20_typical20_problems20_from20_theory20_of20_distributed20_parameter20_systems. and="" was="" initially="" intended="" for="" students="" readers="" primarily="" interested="" in="" applications="" of="" optimal="" control="" ordinary="" differential="" equations.="" this="" vision="" the="" book="" had="" to="" contain="" an="" elementary="" description="" pontryagin="" maximum="" principle="" a="" large="" number="" examples="" from="" various="" fields="" science.="" evolution="" science="" last="" decades="" has="" shown="" that="" its="" _methc2ad_="" ods="" tools="" are="" drawn="" spectrum="" mathematical="" results="" which="" go="" beyond="" classical="" theory="" equations="" real="" _analyc2ad_="" ses.="" areas="" such="" as="" functional="" _analysis2c_="" _topology2c_="" partial="" infinite="" dimensional="" dynamical="" _systems2c_="" _geometry2c_="" played="" will="" continue="" play="" increasing="" role="" development="" sciences.="" on="" other="" _hand2c_="" problems="" is="" rich="" source="" deep="" problems.="" any="" presentation="" sake="" accessibility="" ignores="" these="" facts="" incomplete="" unable="" attain="" goals.="" reason="" we="" considered="" necessary="" widen="" initial="" perspective="" include="" rigorous="" treatment="" processes="" governed="" by="" _ordic2ad_="" nary="" some="" typical="" distributed="" parameter="">
Title:Mathematical Methods in Optimization of Differential SystemsFormat:PaperbackDimensions:262 pagesPublished:October 20, 2012Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9401043272

ISBN - 13:9789401043274

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Table of Contents

Preface. Symbols and Notations. I: Generalized Gradients and Optimality. 1. Fundamentals of Convex Analysis. 2. Generalized Gradients. 3. The Ekeland Variational Principle. II: Optimal Control of Ordinary Differential Systems. 1. Formulation of the Problem and Existence. 2. The Maximum Principle. 3. Applications of the Maximum Principle. III: The Dynamic Programming Method. 1. The Dynamic Programming Equation. 2. Variational and Viscosity Solutions to the Equation of Dynamic Programming. 3. Constructive Approaches to Synthesis Problem IV: Optimal Control of Parameter Distributed Systems. 1. General Description of Parameter Distributed Systems. 2. Optimal Convex Control Problems. 3. The HINFINITY-Control Problem. 4. Optimal Control of Nonlinear Parameter Distributed Systems. Subject Index.