A coherent treatment of nonlinear systems covering chaos, fractals, and bifurcation, as well as equilibrium, stability, and nonlinear oscillations. The systems treated are mostly of difference and differential equations. The author introduces the mathematical properties of nonlinear systems as an integrated theory, rather than simply presenting isolated fashionable topics. The topics are discussed in as concrete a way as possible, worked examples and problems are used to motivate and illustrate the general principles. More advanced parts of the text are denoted by asterisks, thus making it ideally suited to both undergraduate and graduate courses.
This book is written is such a way that the level of mathematical sophistication builds up from chapter to chapter. It has been reorganized into four parts: basic analysis, analysis of feedback systems, advanced analysis, and nonlinear feedback control. Updated content includes subjects which have proven useful in nonlinear control design in recent years—new in the 3rd edition are: expanded treatment of passivity and passivity-based control; integral control, high-gain feedback, recursive methods, optimal stabilizing control, control Lyapunov functions, and observers. For use as a self-study or reference guide by engineers and applied mathematicians.
Papers in this collection partly represent the set of talks that were presented at Texas Tech University on the occasion of Daya’s memorial workshop in the year 2007. Daya had a varied interest in the field of Dynamics and Control Theory and the papers bring out the essence of his involvement in these activities. He also had a large number of collaborators and this collection represent a good fraction of them. The papers included here cover his interest in control theory. Also included are papers from application areas that we believe are of strong interest to him.
This landmark book deals with nonlinear normal modes (NNMs) and nonlinear mode localization. Offers an analysis which enables the study of various nonlinear phenomena having no counterpart in linear theory. On a more theoretical level, the concept of NNMs will be shown to provide an excellent framework for understanding a variety of distinctively nonlinear phenomena such as mode bifurcations and standing or traveling solitary waves.
This study of the nonlinear output regulation problem embraces local as well as global cases, covering such aspects as controller design and practical implementation issues. From the reviews: "The authors treat the problem of output regulation for a nonlinear control system...[they] develop a global approach to output regulation along familiar lines....I found the book to be ambitious and rigorous, tackling some hard conceptual issues." --IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Nonlinear Systems is divided into three volumes. The first deals with modeling and estimation, the second with stability and stabilization and the third with control. This three-volume set provides the most comprehensive and detailed reference available on nonlinear systems. Written by a group of leading experts in the field, drawn from industry, government and academic institutions, it provides a solid theoretical basis on nonlinear control methods as well as practical examples and advice for engineers, teachers and researchers working with nonlinear systems. Each book focuses on the applicability of the concepts introduced and keeps the level of mathematics to a minimum. Simulations and industrial examples drawn from aerospace as well as mechanical, electrical and chemical engineering are given throughout.
Control theory of nonlinear systems, in which either the linear part is known but the relevant nonlinearities in place, kind or parameters are unknown, or both the linear and the nonlinear parts are partially or even most unknown, is a new, demanding and highly interesting field. This book treats the problem by focussing on the role of learning. Intelligent learning techniques are able to determine the unknown components of nonlinear systems. These processes are always stable and convergent. The methods presented can be used both on-line and off-line. They have applications in mechatronics, hydraulics and combustion engines.
The lectures that comprise this volume constitute a comprehensive survey of the many and various aspects of integrable dynamical systems. The present edition is a streamlined, revised and updated version of a 1997 set of notes that was published as Lecture Notes in Physics, Volume 495. This volume will be complemented by a companion book dedicated to discrete integrable systems. Both volumes address primarily graduate students and nonspecialist researchers but will also benefit lecturers looking for suitable material for advanced courses and researchers interested in specific topics.
This book introduces mathematicians to the fascinating mathematical interplay between ideas from stochastics and information theory and practical issues in studying complex multiscale nonlinear systems. It emphasizes the serendipity between modern applied mathematics and applications where rigorous analysis, the development of qualitative and/or asymptotic models, and numerical modeling all interact to explain complex phenomena. After a brief introduction to the emerging issues in multiscale modeling, the book has three main chapters. The first chapter is an introduction to information theory with novel applications to statistical mechanics, predictability, and Jupiter's Red Spot for geophysical flows. The second chapter discusses new mathematical issues regarding fluctuation-dissipation theorems for complex nonlinear systems including information flow, various approximations, and illustrates applications to various mathematical models. The third chapter discusses stochastic modeling of complex nonlinear systems. After a general discussion, a new elementary model, motivated by issues in climate dynamics, is utilized to develop a self-contained example of stochastic mode reduction. Based on A. Majda's Aisenstadt lectures at the University of Montreal, the book is appropriate for both pure and applied mathematics graduate students, postdocs and faculty, as well as interested researchers in other scientific disciplines. No background in geophysical flows is required. About the authors: Andrew Majda is a member of the National Academy of Sciences and has received numerous honors and awards, including the National Academy of Science Prize in Applied Mathematics, the John von Neumann Prize of the Society of Industrial and Applied Mathematics, the Gibbs Prize of the American Mathematical Society, and the Medal of the College de France. In the past several years at the Courant Institute, Majda and a multi-disciplinary faculty have created the Center for Atmosphere Ocean Science to promote cross-disciplinary research with modern applied mathematics in climate modeling and prediction. R.V. Abramov is a young researcher; he received his PhD in 2002. M. J. Grote received his Ph.D. under Joseph B. Keller at Stanford University in 1995.