The purpose of this book is to acquaint the reader with the developments in bilinear systems theory and its applications. Bilinear systems can be used to represent a wide range of physical, chemical, biological, and social systems, as well as manufacturing processes, which cannot be effectively modeled under the assumption of linearity. This book provides a unified approach for the identification and control of nonlinear complex objects that can be transformed into bilinear systems, with a focus on the control of open physical processes functioning in a non-equilibrium mode. A wide class of non-linear control systems can be approximated using novel algorithms motivated by bilinear models. The goal of this book is to describe new methods, heuristics, and optimality criteria with less demanding computational complexity than exact criteria that result in robust adaptive algorithms. Emphasis is placed on three primary disciplines influencing bilinear systems theory: modern differential geometry, control of dynamical systems, and optimization theory.

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