Uniform Output Regulation of Nonlinear Systems : A Convergent Dynamics Approach

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 areas such as s- point control, tracking reference signals and rejecting disturbances generated by an external system, controlled synchronization of dynamical systems, and observer design for autonomous systems. At the moment this is a hot topic in nonlinear control. This book is a result of a four-year research project conducted at the Eindhoven University of Technology. This project, entitled “Robust output regulation for complex dynamical systems,” began with the observation that theproblemofcontrolledsynchronizationofdynamicalsystemscanbecons- ered as a particular case of the output regulation problem. In the beginning of the project, known solutions to the controlled synchronization problem were global and dealt with nonlinear systems having complex (“chaotic”) dyn- ics. At the same time, most of the existing solutions to the nonlinear output regulation problem were local and dealt mostly with exosystems being linear harmonicoscillators. Ourinitialideawas,usingtheresultsfromthecontrolled synchronization problem as a starting point, to extend solutions of the n- linear output regulation problem from the local case to the global case and to avoid restrictive assumptions on the exosystem. As a ?rst step, we started looking for points that were common to these two problems.

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 tobeing 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.