A Course on Optimal Control

Meinsma, Gjerrit, van der Schaft, Arjan

A Course on Optimal Control
  • 出版商: Springer
  • 出版日期: 2024-01-18
  • 售價: $3,300
  • 貴賓價: 9.5 折 $3,135
  • 語言: 英文
  • 頁數: 276
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031366549
  • ISBN-13: 9783031366543

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商品描述

This text provides a detailed and self-contained introduction to the core topics of optimal control for finite-dimensional deterministic dynamical systems. Skillfully designed to guide the student through the development of the subject, the book provides a rich collection of examples, exercises, illustrations, and applications, to support comprehension of the material. Solutions to odd-numbered exercises are included, while a complete set of solutions is available to instructors who adopt the text for their class. The book is adaptable to coursework for final year undergraduates in (applied) mathematics or beginning graduate students in engineering. Required mathematical background includes calculus, linear algebra, a basic knowledge of differential equations, as well as a rudimentary acquaintance with control systems.

The book has developed out of lecture notes that were tested, adapted, and expanded over many years of teaching. Chapters 1-4 constitute thematerial for a basic course on optimal control, covering successively the calculus of variations, minimum principle, dynamic programming, and linear quadratic control. The additional Chapter 5 provides brief views to a number of selected topics related to optimal control, which are meant to peak the reader's interest. Some mathematical background is summarized in Appendix A for easy review. Appendix B recalls some of the basics of differential equations and also provides a detailed treatment of Lyapunov stability theory including LaSalle's invariance principle, as occasionally used in Chapters 3 and 4.

商品描述(中文翻譯)

本書提供了對於有限維確定性動態系統最佳控制核心主題的詳細且自成一體的介紹。書籍巧妙地設計，引導學生逐步理解該主題的發展，並提供豐富的例子、練習題、插圖和應用，以支持對材料的理解。書中包含奇數練習題的解答，並且對於採用本書作為教材的教師提供完整的解答。本書適用於應用數學的大四本科生或工程學的研究生課程。所需的數學背景包括微積分、線性代數、基本的微分方程知識，以及對控制系統有初步了解。

本書是根據多年的教學經驗，經過測試、調整和擴充而成的講義。第1至4章構成了一門關於最佳控制的基礎課程，依次涵蓋變分計算、最小原理、動態規劃和線性二次控制。附加的第5章提供了一些與最佳控制相關的選定主題的簡要介紹，旨在引起讀者的興趣。附錄A對一些數學背景進行了總結，以便輕鬆複習。附錄B回顧了一些微分方程的基礎知識，並提供了對Lyapunov穩定性理論的詳細介紹，包括LaSalle的不變性原理，這在第3和第4章中偶爾會用到。

作者簡介

Gjerrit Meinsma received his graduate degree in Applied Mathematics from the University of Twente (Enschede, the Netherlands) in 1989. Four years later, at the same university, he obtained his Ph.D. degree. His postdoctoral work was done at the University of Newcastle with the Electrical Engineering Department. In 1997 he returned to the University of Twente where he now holds a position of senior lecturer. His research interests are in mathematical systems and control theory, and mathematics in general. He has written around 75 papers. In the last 10 years he focuses more on teaching.

Arjan van der Schaft received his undergraduate and Ph.D. degrees in Mathematics from the University of Groningen, the Netherlands, in 1979 and 1983, respectively. In 1982 he joined the Department of Applied Mathematics, University of Twente, Enschede, where he was appointed as a full professor in Mathematical Systems and Control Theory in 2000. In 2005 he returned to Groningen as a full professor in Mathematics. He is Fellow of the Institute of Electrical and Electronics Engineers (IEEE) and Fellow of the International Federation of Automatic Control (IFAC), and invited semi-plenary speaker at the International Congress of Mathematicians (2006). His research interests include mathematical systems theory, nonlinear control, geometric modeling of multi-physics systems, and hybrid systems. His present focus is on network modeling and control of physical systems and their formulation as port-Hamiltonian systems, and applications in complex engineering systems, power networks, and systems biology.


作者簡介(中文翻譯)

Gjerrit Meinsma於1989年從荷蘭的特溫特大學（Enschede）獲得應用數學的碩士學位。四年後，他在同一所大學獲得了博士學位。他的博士後研究是在紐卡斯爾大學的電機工程系完成的。1997年，他回到特溫特大學，現在擔任高級講師職位。他的研究興趣包括數學系統和控制理論以及數學的其他領域。他已經發表了大約75篇論文。在過去的10年中，他更加關注教學。

Arjan van der Schaft於1979年和1983年分別在荷蘭格羅寧根大學獲得了數學的學士和博士學位。1982年，他加入了特溫特大學應用數學系，並於2000年被任命為數學系統和控制理論的全職教授。2005年，他回到格羅寧根擔任數學的全職教授。他是電機和電子工程師學會（IEEE）和國際自動控制聯合會（IFAC）的會士，並在2006年的國際數學家大會上擔任特邀半專題演講嘉賓。他的研究興趣包括數學系統理論、非線性控制、多物理系統的幾何建模和混合系統。他目前的重點是網絡建模和物理系統的控制，以及將其表述為波特-哈密頓系統，並應用於複雜的工程系統、電力網絡和系統生物學。

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