L2 Gain And Passivity Techniques In Nonlinear Control

With respect to the first edition as Volume 218 in the Lecture Notes in Con trol and Information Sciences series the basic idea of the second edition has remained the same: to provide a compact presentation of some basic ideas in the classical theory of input-output and closed-loop stability, together with a choice of contributions to the recent theory of nonlinear robust and 1foo control and passivity-based control. Nevertheless, some parts of the book have been thoroughly revised and/or expanded, in order to have a more balanced presen tation of the theory and to include some of the new developments which have been taken place since the appearance of the first edition. I soon realized, how ever, that it is not possible to give a broad exposition of the existing literature in this area without affecting the spirit of the book, which is precisely aimed at a compact presentation. So as a result the second edition still reflects very much my personal taste and research interests. I trust that others will write books emphasizing different aspects. Major changes with respect to the first edition are the following: • A new section has been added in Chapter 2 relating L2-gain and passivity via scattering, emphasizing a coordinate-free, geometric, treatment. • The section on stability in Chapter 3 has been thoroughly expanded, also incorporating some recent results presented in [182J.

This standard text gives a unified treatment of passivity and L2-gain theory for nonlinear state space systems, preceded by a compact treatment of classical passivity and small-gain theorems for nonlinear input-output maps. The synthesis between passivity and L2-gain theory is provided by the theory of dissipative systems. Specifically, the small-gain and passivity theorems and their implications for nonlinear stability and stabilization are discussed from this standpoint. The connection between L2-gain and passivity via scattering is detailed. Feedback equivalence to a passive system and resulting stabilization strategies are discussed. The passivity concepts are enriched by a generalised Hamiltonian formalism, emphasising the close relations with physical modeling and control by interconnection, and leading to novel control methodologies going beyond passivity. The potential of L2-gain techniques in nonlinear control, including a theory of all-pass factorizations of nonlinear systems, and of parametrization of stabilizing controllers, is demonstrated. The nonlinear H-infinity optimal control problem is also treated and the book concludes with a geometric analysis of the solution sets of Hamilton-Jacobi inequalities and their relation with Riccati inequalities for the linearization. · L2-Gain and Passivity Techniques in Nonlinear Control (third edition) is thoroughly updated, revised, reorganized and expanded. Among the changes, readers will find: · updated and extended coverage of dissipative systems theory · substantial new material regarding converse passivity theorems and incremental/shifted passivity · coverage of recent developments on networks of passive systems with examples · a completely overhauled and succinct introduction to modeling and control of port-Hamiltonian systems, followed by an exposition of port-Hamiltonian formulation of physical network dynamics · updated treatment of all-pass factorization of nonlinear systems The book provides graduate students and researchers in systems and control with a compact presentation of a fundamental and rapidly developing area of nonlinear control theory, illustrated by a broad range of relevant examples stemming from different application areas.

This standard text gives a unified treatment of passivity and L2-gain theory for nonlinear state space systems, preceded by a compact treatment of classical passivity and small-gain theorems for nonlinear input-output maps. The synthesis between passivity and L2-gain theory is provided by the theory of dissipative systems. Specifically, the small-gain and passivity theorems and their implications for nonlinear stability and stabilization are discussed from this standpoint. The connection between L2-gain and passivity via scattering is detailed. Feedback equivalence to a passive system and resulting stabilization strategies are discussed. The passivity concepts are enriched by a generalised Hamiltonian formalism, emphasising the close relations with physical modeling and control by interconnection, and leading to novel control methodologies going beyond passivity. The potential of L2-gain techniques in nonlinear control, including a theory of all-pass factorizations of nonlinear systems, and of parametrization of stabilizing controllers, is demonstrated. The nonlinear H-infinity optimal control problem is also treated and the book concludes with a geometric analysis of the solution sets of Hamilton-Jacobi inequalities and their relation with Riccati inequalities for the linearization. · L2-Gain and Passivity Techniques in Nonlinear Control (third edition) is thoroughly updated, revised, reorganized and expanded. Among the changes, readers will find: · updated and extended coverage of dissipative systems theory · substantial new material regarding converse passivity theorems and incremental/shifted passivity · coverage of recent developments on networks of passive systems with examples · a completely overhauled and succinct introduction to modeling and control of port-Hamiltonian systems, followed by an exposition of port-Hamiltonian formulation of physical network dynamics · updated treatment of all-pass factorization of nonlinear systems The book provides graduate students and researchers in systems and control with a compact presentation of a fundamental and rapidly developing area of nonlinear control theory, illustrated by a broad range of relevant examples stemming from different application areas.

This book provides techniques to produce robust, stable and useable solutions to problems of H-infinity and H2 control in high-performance, non-linear systems for the first time. The book is of importance to control designers working in a variety of industrial systems. Case studies are given and the design of nonlinear control systems of the same caliber as those obtained in recent years using linear optimal and bounded-norm designs is explained.

This is the second of a series of IFAC Workshops initiated in 2000. The first one chaired and organized by Profs. N. Leonard and R. Ortega, was held in Princeton in March 2000. This proceedings volume looks at the role-played by Lagrangian and Hamiltonian methods in disciplines such as classical mechanics, quantum mechanics, fluid dynamics, electrodynamics, celestial mechanics and how such methods can be practically applied in the control community. *Presents and illustrates new approaches to nonlinear control that exploit the Lagrangian and Hamiltonian structure of the system to be controlled *Highlights the important role of Lagrangian and Hamiltonian Structures as design methods

Over the last 50 years or so, a number of textbooks, monographs and even popular books have been published on nonlinear control theory and design methods. In the area of classical control, for example, there exist books concerned with phase-plane analysis, describing function approach, absolute stability and so on. In the area of modern control there are those related to optimal control, using differential geometry and the differential algebra method, variable structural control, H-infinite control and so on. These books have been useful in promoting the development of automatic control science and technology. Since 1990 there have been many new results and contributions in the area of nonlinear control. This book introduces those topics to interested readers. It will also benefit automation engineers, researchers and scholars in related fields.

This volume is an outgrowth of the workshop "Applications of Advanced Control Theory to Robotics and Automation, "organized in honor of the 70th birthdays of Petar V. Kokotovic and Salvatore (Turi) Nicosia. Both Petar and Turi have carried out distinguished work in the control community and have long been recognized as mentors, as well as experts and pioneers in the field of automatic control, covering many topics in control theory and several different applications. The variety of their research is reflected in this book, which includes contributions ranging from mathematics to laboratory experiments. The scope of the work is very broad, and although each chapter is self-contained, the book has been organized into thematically related chapters, which in some cases, suggest to the reader a convenient reading sequence. The great variety of topics covered and the almost tutorial writing style used by many of the authors will make this book suitable for both experts in the control field and young researchers who seek a more intuitive understanding of these relevant topics in the field.