Generalized Homogeneity in Systems and Control Volume II: Infinite-Dimensional Systems (系統與控制中的廣義均勻性 第二卷：無限維系統)

Polyakov, Andrey

Generalized Homogeneity in Systems and Control Volume II: Infinite-Dimensional Systems
  • 出版商: Springer
  • 出版日期: 2025-02-10
  • 售價: $6,380
  • 貴賓價: 9.5 折 $6,061
  • 語言: 英文
  • 頁數: 366
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031774957
  • ISBN-13: 9783031774959

    • 尚未上市，無法訂購

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商品描述

The second edition of Generalized Homogeneity in Systems and Control is an introduction to the theory of homogeneous systems, useful for the simplification of many types of nonlinear control problem. It propounds methods that can be employed when linearization proves unsuitable and provides a unified approach to stability and robustness analysis, control and observer design, and system discretization.

The second edition splits the coverage of homogeneity, allowing expanded coverage of finite-dimensional systems (in Volume I) and infinite-dimensional systems (in this book). The results are better systematized and easier for readers to study and assimilate.

Generalized Homogeneity in Systems and Control Volume II (second edition) moves from stability analysis to the design of controllers for various systems. Key features of the book include:

  • mathematical models of dynamical systems in infinite-dimensional spaces;
  • the theory of linear dilations in Banach and Hilbert spaces (including Lebesgue and Sobolev spaces);
  • abstract differential equations with homogeneous operators (including differential operators);
  • rewritten, reorganized chapters with the addition of substantial new material;
  • robustness analysis of infinite-dimensional homogeneous systems;
  • homogeneous control in a Hilbert space; and
  • consistent discretization of homogeneous systems.

Illustrative examples - numerical results, computer simulations and real experiments - support all the theoretical material. The coverage of infinite-dimensional systems presented in this book will be of interest to graduate students of control theory and applied mathematics and academic researchers in control.

商品描述(中文翻譯)

《系統與控制中的廣義齊次性》第二版是對齊次系統理論的介紹，對於簡化許多類型的非線性控制問題非常有用。它提出了在線性化不適用時可以採用的方法，並提供了一種統一的穩定性和魯棒性分析、控制和觀察者設計以及系統離散化的方法。

第二版將齊次性的內容分開，使得對有限維系統（在第一卷中）和無限維系統（在本書中）的覆蓋範圍得以擴展。結果更加系統化，讀者更容易學習和理解。

《系統與控制中的廣義齊次性 第二卷》（第二版）從穩定性分析轉向各種系統的控制器設計。書中的主要特點包括：
- 無限維空間中動態系統的數學模型；
- 在Banach和Hilbert空間中的線性擴張理論（包括Lebesgue和Sobolev空間）；
- 具有齊次運算子的抽象微分方程（包括微分運算子）；
- 重新編寫和組織的章節，增加了大量新材料；
- 無限維齊次系統的魯棒性分析；
- 在Hilbert空間中的齊次控制；以及
- 齊次系統的一致離散化。

示例性案例 - 數值結果、計算機模擬和實際實驗 - 支持所有理論材料。本書中呈現的無限維系統的內容將引起控制理論和應用數學的研究生以及控制領域的學術研究者的興趣。

作者簡介

Andrey Polyakov received his PhD in Systems Analysis and Control from the Voronezh State University, Russia in 2005. Until 2010 he was an associate professor with the same university. In 2007 and 2008, he was also a research associate with the CINVESTAV-IPN center in Mexico City. From 2010 up to 2013 he was a leader researcher of the Institute of the Control Sciences, Russian Academy of Sciences. In 2013 he joined Inria, Lille, France as a researcher. He hasco-authored more than 100 papers in peer-reviewed journals and three books Attractive Ellipsoids in Robust Control, Road Map for Sliding Mode Control Design and Generalized Homogeneity in Systems and Control 1st Ed. His research interests include various aspects of nonlinear control and estimation theory such as finite-time/fixed-time control, generalized homogeneity and Lyapunov methods for both finite-dimensional and infinite-dimensional systems.

作者簡介(中文翻譯)

安德烈·波利亞科夫（Andrey Polyakov）於2005年在俄羅斯沃羅涅什國立大學獲得系統分析與控制的博士學位。直到2010年，他一直擔任該大學的副教授。在2007年和2008年，他也曾在墨西哥城的CINVESTAV-IPN中心擔任研究助理。從2010年到2013年，他是俄羅斯科學院控制科學研究所的首席研究員。2013年，他加入法國里爾的Inria擔任研究員。他共同撰寫了超過100篇同行評審期刊的論文以及三本書籍《穩健控制中的吸引橢圓體》（Attractive Ellipsoids in Robust Control）、《滑模控制設計的路線圖》（Road Map for Sliding Mode Control Design）和《系統與控制中的廣義齊次性》（Generalized Homogeneity in Systems and Control）第一版。他的研究興趣包括非線性控制和估計理論的各個方面，如有限時間/固定時間控制、廣義齊次性以及針對有限維和無限維系統的李雅普諾夫方法。

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