Time optimal control of evolution equations. (2018)

• Record Type: Book
• Further Information: Note: Gengsheng Wang, Lijuan Wang, Yashan Xu, Yubiao Zhang.
• Authors: Wang, Gengsheng; Wang, Lijuan; Xu, Yashan; Zhang, Yubiao
• Contents: Intro; Preface; Acknowledgments; Contents; Acronyms; 1 Mathematical Preliminaries; 1.1 Elements in Functional Analysis; 1.1.1 Spaces and Operators; 1.1.2 Some Geometric Aspects of Banach Spaces; 1.1.3 Semigroups and Evolution Equations; 1.1.4 Minimization of Functionals; 1.2 Set-Valued Map; 1.3 Controllability and Observability Estimate; Miscellaneous Notes; References; 2 Time Optimal Control Problems; 2.1 Overview on Time Optimal Control Problems; 2.1.1 Introduction; 2.1.2 Different Ingredients in Time Optimal Control Problems; 2.2 Connections of Minimal and Maximal Time Controls 2.3 Several Examples2.4 Main Subjects on Time Optimal Control Problems; Miscellaneous Notes; References; 3 Existence of Admissible Controls and Optimal Controls; 3.1 Admissible Controls and Controllability; 3.1.1 General Results in Abstract Setting; 3.1.2 Linear ODEs with Ball-Type Control Constraints; 3.1.3 Heat Equations with Ball-Type Control Constraints; 3.2 Admissible Controls and Minimal Norm Problems; 3.2.1 General Results in Abstract Setting; 3.2.2 Heat Equations with Ball-Type Control Constraints; 3.3 Admissible Controls and Reachable Sets; 3.3.1 General Results in Abstract Setting 3.3.2 Reachable Sets of Linear ODEs3.4 Existence of Optimal Controls; 3.4.1 Existence of Optimal Controls for Regular Cases; 3.4.2 Existence of Optimal Controls for Blowup Case; Miscellaneous Notes; References; 4 Maximum Principle of Optimal Controls; 4.1 Classical Maximum Principle of Minimal Time Controls; 4.1.1 Geometric Intuition; 4.1.2 Classical Maximum Principle; 4.1.3 Conditions on Separation in Classical Maximum Principle; 4.2 Local Maximum Principle and Minimal Time Controls; 4.2.1 Some Properties on Controllable Sets and Reachable Sets; 4.2.2 Separability and Local Maximum Principle 4.2.3 Conditions on Separation in Local Maximum Principle4.3 Weak Maximum Principle and Minimal Time Controls; 4.3.1 Separability and Weak Maximum Principle; 4.3.2 Two Representation Theorems Related to the Separability; 4.3.3 Conditions on Separation in Weak Maximum Principle; 4.4 Maximum Principle for Maximal Time Controls; 4.4.1 Classical Maximum Principle for Maximal Time Controls; 4.4.2 Local Maximum Principle for Maximal Time Controls; Miscellaneous Notes; References; 5 Equivalence of Several Kinds of Optimal Controls 5.1 Minimal Time Controls, Minimal Norm Controls, and Time Invariant Systems5.2 Minimal Time Controls, Minimal Norm Controls, and Time-Varying Systems: Part I; 5.2.1 Properties of Minimal Time and Minimal Norm Functions; 5.2.2 Proof of the Main Result; 5.3 Minimal Time Controls, Minimal Norm Controls, and Time-Varying Systems: Part II; 5.4 Maximal Time, Minimal Norm, and Optimal Target Controls; 5.4.1 Existence of Optimal Controls for These Problems; 5.4.2 Connections Between Problems of Optimal Target Control and Minimal Norm Control
• Publisher Details: Cham, Switzerland : Birkhäuser
• Publication Date: 2018
• Extent: 1 online resource, illustrations
• Subjects: 515/.35; Mathematics; Evolution equations; Control theory; MATHEMATICS / Calculus; MATHEMATICS / Mathematical Analysis; Technology & Engineering -- Automation; Technology & Engineering -- Engineering (General); Automatic control engineering; Maths for engineers; Systems theory; Engineering mathematics; Science -- System Theory; Cybernetics & systems theory; Electronic books
• Languages: English
• ISBNs: 9783319953632
• Related ISBNs: 331995363X; 9783319953625
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (SpringerLink, viewed August 29, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.