Andrey Polyakov - Böcker

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; andexperiments 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.

This book is devoted to control of finite and infinite dimensional processes with continuous-time and discrete time control, focusing on suppression problems and new methods of adaptation applicable for systems with sliding motions only.

This book is an introduction to the theory of homogeneous systems, useful for the simplification of many types of nonlinear control problems. 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 this book) and infinite-dimensional systems (in Volume II). The results are better systematized and easier for readers to study and assimilate.The first volume details the concepts of finite-time and fixed-time stability. Key features of the book include:mathematical models of dynamical systems in finite-dimensional spaces;the theory of linear dilations in Euclidean spaces;homogeneous control and estimation;extensively expanded and original chapters with entirely new treatments of digitization, safety-critical systems, neural networks, and multiagent control;simple methods for an upgrade of existing linear control laws;numerical schemes for a consistent digital implementation of homogeneous algorithms; andexperimental results that confirm an improvement of PID controllers.Illustrative examples—numerical results, computer simulations, and real experiments—support all the theoretical material. The coverage of finite-dimensional systems presented in this book is of interest to graduate students of control theory from engineering and applied-mathematical backgrounds and to practising control engineers.

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.

Attractive Ellipsoids in Robust Control