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Generalized Homogeneity in Systems and Control

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Generalized Homogeneity in Systems and Control/ by Andrey Polyakov.
Author:	Polyakov, Andrey.
Description:	XVIII, 447 p. 52 illus., 33 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Control engineering. -
Online resource:	https://doi.org/10.1007/978-3-030-38449-4
ISBN:	9783030384494

Generalized Homogeneity in Systems and Control
Polyakov, Andrey.

Generalized Homogeneity in Systems and Control[electronic resource] /by Andrey Polyakov. - 1st ed. 2020. - XVIII, 447 p. 52 illus., 33 illus. in color.online resource. - Communications and Control Engineering,0178-5354. - Communications and Control Engineering,.

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.

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.

ISBN: 9783030384494

Standard No.: 10.1007/978-3-030-38449-4doiSubjects--Topical Terms:

1249728
Control engineering.

LC Class. No.: TJ212-225

Dewey Class. No.: 629.8

Generalized Homogeneity in Systems and Control
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520 $a 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.
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