Mathematical Systems Theory III: Linear Quadratic Control and Adaptive Feedback
暫譯: 數學系統理論 III：線性二次控制與自適應反饋

Hinrichsen, Diederich, Pritchard, Anthony J., Colonius, Fritz

Mathematical Systems Theory III: Linear Quadratic Control and Adaptive Feedback
  • 出版商: Springer
  • 出版日期: 2026-02-06
  • 售價: $2,810
  • 貴賓價: 9.8 折 $2,753
  • 語言: 英文
  • 頁數: 425
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3032084008
  • ISBN-13: 9783032084002
  • 相關分類: 控制系統 Control-systems

    • 海外代購書籍(需單獨結帳)

商品描述

This is the third and final volume of Mathematical Systems Theory. Like the preceding volumes, it presents the mathematical foundations of systems and control theory in a self-contained, comprehensive, detailed, and mathematically rigorous manner. The exposition proceeds from the very general to the more specific, with rigorous mathematics complemented by numerous illustrations and explanatory remarks.

Volume III comprises two chapters and an appendix. In contrast to the first two volumes, only continuous-time systems are considered here. Chapter 9 addresses linear-quadratic optimal control and the Riccati equation, while Chapter 10 deals with zero dynamics and adaptive feedback regulation. Distinctive features include:

- a comprehensive treatment of the linear-quadratic optimal control problem

- a presentation of the bounded real and the Kalman-Yakubovich-Popov Lemma

- a systematic development of spectral factorization

- a study of the relative degree in state space and frequency domain

- a detailed exposition of the Byrnes-Isidori form and zero dynamics

- a development of the fundamentals of high-gain adaptive and funnel control.

The book combines the characteristics of a detailed introductory textbook with those of a reference source. The material should be accessible to mathematics students after two years of study, as well as to engineering students with a strong mathematical background. It will be of value to researchers in systems theory, as well as to mathematicians and engineers seeking to acquire a solid understanding of the mathematical foundations of the topics outlined above.

商品描述(中文翻譯)

這是《數學系統理論》的第三卷也是最後一卷。與前兩卷類似，本卷以自成體系、全面、詳細且數學上嚴謹的方式呈現系統與控制理論的數學基礎。內容從非常一般的概念逐漸深入到更具體的主題，嚴謹的數學論述輔以大量的插圖和解釋性註釋。

第三卷包含兩個章節和一個附錄。與前兩卷不同，本卷僅考慮連續時間系統。第九章探討線性-二次最優控制及Riccati方程，而第十章則處理零動態和自適應反饋調節。其特點包括：

- 對線性-二次最優控制問題的全面處理
- 對有界實數和Kalman-Yakubovich-Popov引理的介紹
- 對譜因式分解的系統性發展
- 在狀態空間和頻域中對相對階的研究
- 對Byrnes-Isidori形式和零動態的詳細闡述
- 對高增益自適應控制和漏斗控制基本原理的發展

本書結合了詳細入門教科書的特點和參考資料的特性。這些材料應該對學習兩年數學的學生以及具有堅實數學背景的工程學生是可接觸的。對於系統理論的研究人員，以及希望深入理解上述主題數學基礎的數學家和工程師，本書將具有重要價值。

作者簡介

Diederich Hinrichsen is a retired Professor of Mathematical Systems Theory at the University of Bremen.

Anthony J. Pritchard (+ 2007) was Professor of Mathematics and founder and director of the Control Theory Centre at the University of Warwick.

Fritz Colonius is a retired Professor of Applied Mathematics at the University of Augsburg. His main research interest is the interplay of control theory and dynamical systems theory.

Tobias Damm is Professor for Systems and Control Theory at RPTU University Kaiserslautern-Landau. His research interests include linear algebra and numerical analysis and the application of these to control theory.

Achim Ilchmann held a chair in Applied Mathematics at the Technical University of Ilmenau until his retirement in 2022. His research interests include the algebraic theory of time-varying linear systems, adaptive control, and Baroque architecture.

Birgit Jacob has been with the University of Wuppertal, Germany, since 2010, where she is a full professor in analysis. Her current research interests include the area of infinite-dimensional systems and operator theory, particularly well-posed linear systems and port-Hamiltonian systems.

Fabian R. Wirth is Professor for Dynamical Systems at the University of Passau. His research interests include stability theory, switched systems, infinite-dimensional and large-scale systems.

作者簡介(中文翻譯)

迪德里希·欣里克森（Diederich Hinrichsen）是不來梅大學（University of Bremen）退休的數學系統理論教授。安東尼·J·普里查德（Anthony J. Pritchard，2007年逝世）曾任華威大學（University of Warwick）數學教授及控制理論中心的創始人和主任。弗里茨·科洛尼烏斯（Fritz Colonius）是奧格斯堡大學（University of Augsburg）退休的應用數學教授。他的主要研究興趣是控制理論與動態系統理論之間的相互作用。托比亞斯·達姆（Tobias Damm）是凱瑟斯勞滕-蘭道應用科技大學（RPTU University Kaiserslautern-Landau）系統與控制理論教授。他的研究興趣包括線性代數和數值分析，以及這些在控制理論中的應用。阿希姆·伊爾赫曼（Achim Ilchmann）在伊爾梅瑙科技大學（Technical University of Ilmenau）擔任應用數學教授，直到2022年退休。他的研究興趣包括時間變化線性系統的代數理論、自適應控制和巴洛克建築。比爾吉特·雅各布（Birgit Jacob）自2010年以來一直在德國伍珀塔爾大學（University of Wuppertal）任職，現為分析學的全職教授。她目前的研究興趣包括無限維系統和算子理論，特別是良定義的線性系統和端口哈密頓系統。法比安·R·維爾特（Fabian R. Wirth）是帕紹大學（University of Passau）的動態系統教授。他的研究興趣包括穩定性理論、切換系統、無限維系統和大規模系統。

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