Overview
- Unifies recent results in time-optimal control into a new framework for minimal and maximal time-optimal control problems
- Introduces three different types of Pontryagin’s maximum principles from geometric points of view
- Provides examples of control problems for a variety of dynamical systems to demonstrate applications of time-optimal control
- Discusses different ways of using the bang-bang property in finite and infinite dimensional cases
Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 92)
Part of the book sub series: PNLDE Subseries in Control (PNLDE-SC)
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Table of contents (6 chapters)
Keywords
About this book
This monograph develops a framework for time-optimal control problems, focusing on minimal and maximal time-optimal controls for linear-controlled evolution equations. Its use in optimal control provides a welcome update to Fattorini’s work on time-optimal and norm-optimal control problems. By discussing the best way of representing various control problems and equivalence among them, this systematic study gives readers the tools they need to solve practical problems in control.
After introducing preliminaries in functional analysis, evolution equations, and controllability and observability estimates, the authors present their time-optimal control framework, which consists of four elements: a controlled system, a control constraint set, a starting set, and an ending set. From there, they use their framework to address areas of recent development in time-optimal control, including the existence of admissible controls and optimal controls, Pontryagin’s maximum principlefor optimal controls, the equivalence of different optimal control problems, and bang-bang properties.This monograph will appeal to researchers and graduate students in time-optimal control theory, as well as related areas of controllability and dynamic programming. For ease of reference, the text itself is self-contained on the topic of time-optimal control. Frequent examples throughout clarify the applications of theorems and definitions, although experience with functional analysis and differential equations will be useful.
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Authors and Affiliations
About the authors
Lijuan Wang is a professor at Wuhan University's School of Matheamtics and Statistics.
Yashan Xu is a professor at the School of Mathematical University at Fudan University.
Yubiao Zhang is a professor at the Center for Applied Mathematics at Tianjin University.
Bibliographic Information
Book Title: Time Optimal Control of Evolution Equations
Authors: Gengsheng Wang, Lijuan Wang, Yashan Xu, Yubiao Zhang
Series Title: Progress in Nonlinear Differential Equations and Their Applications
DOI: https://doi.org/10.1007/978-3-319-95363-2
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG, part of Springer Nature 2018
Hardcover ISBN: 978-3-319-95362-5Published: 31 August 2018
Softcover ISBN: 978-3-030-07021-2Published: 13 December 2018
eBook ISBN: 978-3-319-95363-2Published: 22 August 2018
Series ISSN: 1421-1750
Series E-ISSN: 2374-0280
Edition Number: 1
Number of Pages: XVI, 334
Number of Illustrations: 2 b/w illustrations, 2 illustrations in colour
Topics: Systems Theory, Control, Control and Systems Theory, Engineering Mathematics