Uniform Output Regulation of Nonlinear Systems

Abstract

The problem of asymptotic regulation of the output of a dynamical system plays a central role in control theory. An important variant of this problem is the output regulation problem, which can be used in such areas as set-point control, tracking reference signals and rejecting disturbances generated by an external system, controlled synchronization of dynamical systems, and observer design for autonomous systems. This book is one of the first systematic studies on the nonlinear output regulation problem that embraces both the local and global solvability analysis, covering such aspects as solvability conditions, controller design, and practical implementation issues. The book opens with the development of the mathematical apparatus of convergent systems—very useful for studying nonlinear control systems—laying the foundation for most of the results presented in the work. The study then proceeds to a new problem statement—the so-called uniform output regulation problem. A comprehensive solvability analysis of this problem is provided in the next part of the work. Based on the solvability analysis, constructive controller design methods for the global uniform output regulation problem are presented for various classes of nonlinear systems. In an attempt to bridge the gap between theory and practice, the authors conclude with a presentation of an experimental case study. The experiment—one of the first in the field of nonlinear output regulation—deals with control of a translational oscillator with a rotational actuator, illustrating the applicability of the nonlinear output regulation theory in experiments and raising a number of questions to be addressed in future research. The scope of questions addressed in the book, the uniformity of their treatment, the novelty of the proposed approach, and the obtained results make this volume unique with respect to other works on the problem of nonlinear output regulation. In addition to being an excellent reference for the uniform output regulation problem, the book has a tutorial value on convergent systems. The work will be of interest to control engineers, theorists, and students, and may be used as a textbook for a graduate course on nonlinear control.