变分法和最优控制论

图书标准信息

• 作者 [美]利伯逊（Daniel Liberzon） 著
• 出版社 世界图书出版公司
• 出版时间 2013-10
• 版次 1
• ISBN 9787510061417
• 定价 59.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 235页
• 正文语种 英语
• 丛书 经典教学丛书

【内容简介】

　　ThisbookgrewoutofmylecturenotesforagraduatecourseonoptimalcontroltheorywhichItaughtattheUniversityofIllinoisatUrbana-Champaignduringtheperiodfrom2005to2010.Whilepreparingthelectures，Ihaveaccumulatedanentireshelfoftextbooksoncalculusofvariationsandoptimalcontrolsystems.

【目录】

Preface

1Introduction
1.1Optimalcontrolproblem
1.2Somebackgroundonfinite-dimensionaloptimization
1.2.1Unconstrainedoptimization
1.2.2Constrainedoptimization
1.3Previewofinfinite-dimensionaloptimization
1.3.1Functionspaces,norms,andlocalminima
1.3.2Firstvariationandfirst-ordernecessarycondition
1.3.3Secondvariationandsecond-orderconditions
1.3.4Globalminimaandconvexproblems
1.4NotesandreferencesforChapter1

2CalculusofVariations
2.1Examplesofvariationalproblems
2.1.1Dido'sisoperimetricproblem
2.1.2Lightrefiectionandrefraction
2.1.3Catenary
2.1.4Brachistochrone
2.2Basiccalculusofvariationsproblem
2.2.1Weakandstrongextrema
2.3First-ordernecessaryconditionsforweakextrema
2.3.1Euler-Lagrangeequation
2.3.2Historicalremarks
2.3.3Technicalremarks
2.3.4Twospecialcases
2.3.5Variable-endpointproblems
2.4Hanultonianformalismandmechanics
2.4.1Hamilton'scanonicalequations
2.4.2Legendretransformation
2.4.3Principleofleastactionandconservationlaws
2.5Variationalproblemswithconstraints
2.5.1Integralconstraints
2.5.2Non-integralconstraints
2.6Second-orderconditions
2.6.1Legendre'snecessaryconditionforaweakminimum
2.6.2Sufficientconditionforaweakminimum
2.7NotesandreferencesforChapter2

3WomCalculusofVariationstoOptimalControl
3.1Necessaryconditionsforstrongextrema
3.1.1Weierstrass-Erdmanncornerconditions
3.1.2Weierstrassexcessfunction
3.2Calculusofvariationsversusoptimalcontrol
3.3Optimalcontrolproblemformulationandas8umptions
3.3.1Controlsystem
3.3.2Costfunctional
3.3.3Targetset
3.4Variationalapproachtothefixed-time,free-endpointproblem
3.4.1Preliminaries
3.4.2Firstvariation
3.4.3Secondvariation
3.4.4Somecomments
3.4.5Critiqueofthevariationalapproachandpreviewofthemaximumprinciple
3.5NotesandreferencesforChapter3
……

4TheMaximumPrinciple
5TheHamilton-Jacobi-BellmanEquation
6TheLinearQuadraticRegulator
7AdvancedTopics

Bibliography
Index