Generalized Homogeneity in Systems and Control

Andrey Polyakov

Feb. 2020 · Springer Nature

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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.

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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.

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