Generalized Homogeneity in Systems and Control

Andrey Polyakov (Autor)

Buch | Hardcover

XVIII, 447 Seiten

2020 | 1st ed. 2020
Springer International Publishing (Verlag)
978-3-030-38448-7 (ISBN)

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lt;p>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.

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.

Chapter 1. Introduction.- Part I: Models of Control Systems and Stability Analysis.- Chapter 2. Finite-Dimensional Models.- Chapter 3. Infinite-Dimensional Models.- Chapter 4. Stability and Convergence Rate.- Chapter 5. Method of Lyapunov Functions.- Part II: Homogeneous Control Systems.- Chapter 6. Dilation Groups in Banach, Hilbert and Euclidean Spaces.- Chapter 7. Homogeneous Mappings.- Chapter 8. Analysis of Homogeneous Dynamical Systems.- Chapter 9. Homogeneous Stabilization.- Chapter 10. Consistent Discretization of Homogeneous Models.- Chapter 11. Homogeneous State Estimation.- Chapter 12. Homogeneous Optimal Control.- Appendix.- Index.

Erscheinungsdatum	18.02.2020
Reihe/Serie	Communications and Control Engineering
Zusatzinfo	XVIII, 447 p. 52 illus., 33 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	935 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Technik ► Elektrotechnik / Energietechnik
Schlagworte	Approximation of Nonlinear Systems • Dilation Symmetry • Finite Time Stability • Homogeneous Systems • infinite dimensional systems • Linear Dilations • Nonlinear Control • Nonlinear Estimation • Stability of Nonlinear Systems
ISBN-10	3-030-38448-9 / 3030384489
ISBN-13	978-3-030-38448-7 / 9783030384487
Zustand	Neuware