Time Optimal Control of Evolution Equations

  • Gengsheng Wang
  • Lijuan Wang
  • Yashan Xu
  • Yubiao Zhang

Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 92)

Also part of the PNLDE Subseries in Control book sub series (PNLDE-SC, volume 92)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Gengsheng Wang, Lijuan Wang, Yashan Xu, Yubiao Zhang
    Pages 1-35
  3. Gengsheng Wang, Lijuan Wang, Yashan Xu, Yubiao Zhang
    Pages 37-64
  4. Gengsheng Wang, Lijuan Wang, Yashan Xu, Yubiao Zhang
    Pages 65-123
  5. Gengsheng Wang, Lijuan Wang, Yashan Xu, Yubiao Zhang
    Pages 125-203
  6. Gengsheng Wang, Lijuan Wang, Yashan Xu, Yubiao Zhang
    Pages 205-279
  7. Gengsheng Wang, Lijuan Wang, Yashan Xu, Yubiao Zhang
    Pages 281-329
  8. Back Matter
    Pages 331-334

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 principle for 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.


time optimal controls linear evolution equations bang-bang properties of optimal groups the Cauchy problem equivalence of optimal controls Pontryagin Maximum Principle bang-bang property

Authors and affiliations

  • Gengsheng Wang
    • 1
  • Lijuan Wang
    • 2
  • Yashan Xu
    • 3
  • Yubiao Zhang
    • 4
  1. 1.Center for Applied MathematicsTianjin UniversityTianjinChina
  2. 2.School of Mathematics and StatisticsWuhan UniversityWuhanChina
  3. 3.School of Mathematical SciencesFudan UniversityShanghaiChina
  4. 4.Center for Applied MathematicsTianjin UniversityTianjinChina

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-95362-5
  • Online ISBN 978-3-319-95363-2
  • Series Print ISSN 1421-1750
  • Series Online ISSN 2374-0280
  • Buy this book on publisher's site