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L2-Gain and Passivity Techniques in Nonlinear Control (Communications and Control Engineering) Hardcover - 2016

Name: L2-Gain and Passivity Techniques in Nonlinear Control
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Author: Arjan van der Schaft
ISBN: 9783319499918

by van der Schaft, Arjan

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From the publisher

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.

From the rear cover

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.

Details

Title L2-Gain and Passivity Techniques in Nonlinear Control (Communications and Control Engineering)
Author van der Schaft, Arjan
Binding Hardcover
Publisher Springer
Date 2016
ISBN 9783319499918

About the author

A.J. (Arjan) van der Schaft (1955) received the undergraduate and Ph.D. degrees in Mathematics from the University of Groningen, The Netherlands, in 1979 and 1983, respectively. In 1982 he joined the Department of Applied Mathematics, University of Twente, Enschede, where he was appointed as a full professor in Mathematical Systems and Control Theory in 2000. In September 2005 he returned to Groningen as a full professor in Mathematics.

He has served as Associate Editor for Systems & Control Letters, Journal of Nonlinear Science, SIAM Journal on Control and Optimization, IEEE Transactions on Automatic Control and the European Journal of Control. Currently he is on the Editorial Board for the Journal of Geometric Mechanics and Annual Reviews in Control.

Arjan van der Schaft is Fellow of the Institute of Electrical and Electronics Engineers (IEEE) and of the International Federation of Automatic Control (IFAC). He was Invited Lecturer at the International Congress of Mathematicians, Madrid, Spain, 2006. He is the 2013 recipient of the 3-yearly awarded Certificate of Excellent Achievements) of the IFAC Technical Committee on Nonlinear Systems.

Arjan van der Schaft is (co-)author of the following other books: System Theoretic Descriptions of Physical Systems (1984), Variational and Hamiltonian Control Systems (1987, with P.E. Crouch), Nonlinear Dynamical Control Systems (1990, with H. Nijmeijer), An Introduction to Hybrid Dynamical Systems (2000, with J.M. Schumacher), Modeling and Control of Complex Physical Systems: the Port-Hamiltonian Approach( Geoplex Consortium, 2009), and Port-Hamiltonian Systems Theory: An Introductory Overview (2014, with D. Jeltsema). He (co-)edited five conference proceedings.

He (co-)authored around 125 journal articles and 265 refereed contributions to proceedings or book chapters.