- Provides a thorough introduction to the theory of generalized homogeneous systems
- Discusses mathematical models of dynamic systems in finite- and infinite-dimensions
- Supports all theory with illustrations, examples and simulations
- Shows engineers how to enhance the precision of PID control
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- About this book
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This monograph introduces the theory of generalized homogeneous systems governed by differential equations in both Euclidean (finite-dimensional) and Banach/Hilbert (infinite-dimensional) spaces. It develops methods of stability and robustness analysis, control design, state estimation and discretization of homogeneous control systems. Generalized Homogeneity in Systems and Control is structured in two parts. Part I discusses various models of control systems and related tools for their analysis, including Lyapunov functions. Part II deals with the analysis and design of homogeneous control systems. Some of the key features of the text include:
- mathematical models of dynamical systems in finite-dimensional and infinite-dimensional spaces;
- the theory of linear dilations in Banach spaces;
- homogeneous control and estimation;
- simple methods for an "upgrade" of existing linear control laws;
- numerical schemes for a consistent digital implementation of homogeneous algorithms; and
- experiments confirming an improvement of PID controllers.
The advanced mathematical material will be of interest to researchers, mathematicians working in control theory and mathematically oriented control engineers.
- About the authors
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Andrey Polyakov received his Ph.D. degree in Systems Analysis and Control from Voronezh State University in 2005, where he then acted as Assistant Professor until from 2008 to 2010. In 2007-2008, Dr Polyakov worked at CINVESTAV in Mexico. From 2010 to 2013, he was Lead Researcher of the Institute of the Control Sciences, Russian Academy of Sciences. Since 2013 he has been working at the NON-A team of Inria in Lille, France. His main research interests include mathematical methods in robust and nonlinear control. He has authored or co-authored over 150 publications, including the book Attractive Ellipsoids in Robust Control. He was the editor of the International Journal of Robust and Nonlinear Control, Journal of Optimization Theory and Applications (JOTA), and Automation and Remote Control.
- Table of contents (12 chapters)
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Introduction
Pages 1-21
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Finite-Dimensional Models
Pages 25-50
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Infinite-Dimensional Models
Pages 51-110
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Stability and Convergence Rate
Pages 111-120
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Method of Lyapunov Functions
Pages 121-149
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Table of contents (12 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Generalized Homogeneity in Systems and Control
- Authors
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- Andrey Polyakov
- Series Title
- Communications and Control Engineering
- Copyright
- 2020
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer Nature Switzerland AG
- eBook ISBN
- 978-3-030-38449-4
- DOI
- 10.1007/978-3-030-38449-4
- Hardcover ISBN
- 978-3-030-38448-7
- Series ISSN
- 0178-5354
- Edition Number
- 1
- Number of Pages
- XVIII, 447
- Number of Illustrations
- 19 b/w illustrations, 33 illustrations in colour
- Topics
