Generalized Homogeneity in Systems and Control Volume I

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; and
• experimental 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.

Andrey Polyakov received his Ph.D. in Systems Analysis and Control from the Voronezh State University, Russia in 2005. Until 2010, he was an associate professor at the same university. In 2007 and 2008, he was also a research associate with the CINVESTAV-IPN center in Mexico City. From 2010 up to 2013, he was a leader researcher at the Institute of the Control Sciences, Russian Academy of Sciences. In 2013, he joined Inria, Lille, France, as a researcher. He has co-authored more than 100 papers in peer-reviewed journals and three books Attractive Ellipsoids in Robust Control, Road Map for Sliding Mode Control Design and Generalized Homogeneity in Systems and Control 1st Ed. His research interests include various aspects of nonlinear control and estimation theory such as finite-time/fixed-time control, generalized homogeneity, and Lyapunov methods for both finite-dimensional and infinite-dimensional systems.