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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.

What do phone rates, frequent flyer programs, and railroad tariffs all have in common? They are all examples of nonlinear pricing. Pricing is nonlinear when it is not strictly proportional to the quantity purchased. The Electric Power Research Institute has commissioned Robert Wilson to review the various facets of nonlinear pricing. The work starts with a general non-mathematical discussion, followed by a more technical presentation intended for readers with a fairly advanced background. Thorough and detailed, this study has ample examples of case studies from a variety of industries.

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This is the second of a five-volume exposition of the main principles of nonlinear functional analysis and its applications to the natural sciences, economics, and numerical analysis. The presentation is self -contained and accessible to the nonspecialist. Part II concerns the theory of monotone operators. It is divided into two subvolumes, II/A and II/B, which form a unit. The present Part II/A is devoted to linear monotone operators. It serves as an elementary introduction to the modern functional analytic treatment of variational problems, integral equations, and partial differential equations of elliptic, parabolic and hyperbolic type. This book also represents an introduction to numerical functional analysis with applications to the Ritz method along with the method of finite elements, the Galerkin methods, and the difference method. Many exercises complement the text. The theory of monotone operators is closely related to Hilbert's rigorous justification of the Dirichlet principle, and to the 19th and 20th problems of Hilbert which he formulated in his famous Paris lecture in 1900, and which strongly influenced the development of analysis in the twentieth century.

Design techniques for nonlinear microwave circuits are much less developed than for linear microwave circuits. Until now there has been no up-to-date text available in this area. Current titles in this field are considered outdated and tend to focus on analysis, failing to adequately address design and measurement aspects. Giannini and Leuzzi provide the theoretical background to non-linear microwave circuits before going on to discuss the practical design and measurement of non-linear circuits and components. Non-linear Microwave Circuit Design reviews all of the established analysis and characterisation techniques available and provides detailed coverage of key modelling methods. Practical examples are used throughout the text to emphasise the design and application focus of the book. * Provides a unique, design-focused, coverage of non-linear microwave circuits * Covers the fundamental properties of nonlinear circuits and methods for device modelling * Outlines non-linear measurement techniques and characterisation of active devices * Reviews available design methodologies for non-linear power amplifiers and details advanced software modelling tools * Provides the first detailed treatment of non-linear frequency multipliers, mixers and oscillators * Focuses on the application potential of non-linear components Practicing engineers and circuit designers working in microwave and communications engineering and designing new applications, as well as senior undergraduates, graduate students and researchers in microwave and communications engineering and their libraries will find this a highly rewarding read.

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Nonlinear physics continues to be an area of dynamic modern research, with applications to physics, engineering, chemistry, mathematics, computer science, biology, medicine and economics. In this text extensive use is made of the Mathematica computer algebra system. No prior knowledge of Mathematica or programming is assumed. This book includes 33 experimental activities that are designed to deepen and broaden the reader's understanding of nonlinear physics. These activities are correlated with Part I, the theoretical framework of the text.

This instructive book introduces the key ideas behind practical nonlinear optimization, accompanied by computational examples and supporting software. It combines computational finance with an important class of numerical techniques.

Filling a void in chemical engineering and optimization literature, this book presents the theory and methods for nonlinear and mixed-integer optimization, and their applications in the important area of process synthesis. Other topics include modeling issues in process synthesis, and optimization-based approaches in the synthesis of heat recovery systems, distillation-based systems, and reactor-based systems. The basics of convex analysis and nonlinear optimization are also covered and the elementary concepts of mixed-integer linear optimization are introduced. All chapters have several illustrations and geometrical interpretations of the material as well as suggested problems. Nonlinear and Mixed-Integer Optimization will prove to be an invaluable source--either as a textbook or a reference--for researchers and graduate students interested in continuous and discrete nonlinear optimization issues in engineering design, process synthesis, process operations, applied mathematics, operations research, industrial management, and systems engineering.

For a first course on nonlinear control that can be taught in one semester ¿ This book emerges from the award-winning book, Nonlinear Systems, but has a distinctly different mission and¿organization. While Nonlinear Systems was intended as a reference and a text on nonlinear system analysis and its application to control, this streamlined book is intended as a text for a first course on nonlinear control. In Nonlinear Control, author Hassan K. Khalil employs a writing style that is intended to make the book accessible to a wider audience without compromising the rigor of the presentation. ¿ Teaching and Learning Experience This program will provide a better teaching and learning experience–for you and your students. It will help: Provide an Accessible Approach to Nonlinear Control: This streamlined book is intended as a text for a first course on nonlinear control that can be taught in one semester. Support Learning: Over 250 end-of-chapter exercises give students plenty of opportunities to put theory into action.

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This text has been especially written for advanced undergraduate students in mathematics, applied mathematics, engineering and, to a lesser extent, chemistry and physics. In writing the text, the author recognises and attempts to bridge the gap which exists between standard elementary courses on differential equations and advanced graduate courses on dynamical systems and chaotic motion. The text is concerned wih nonlinear differential equations and the use of perturbation methods to reveal the subtle effects that even small nonlinear terms can produce. The emphasis of the text is on stability, nonlinearity and perturbation methods.

Bridging the gap between elementary courses and the research literature in this field, the book covers the basic concepts necessary to study differential equations. Stability theory is developed, starting with linearisation methods going back to Lyapunov and Poincaré, before moving on to the global direct method. The Poincaré-Lindstedt method is introduced to approximate periodic solutions, while at the same time proving existence by the implicit function theorem. The final part covers relaxation oscillations, bifurcation theory, centre manifolds, chaos in mappings and differential equations, and Hamiltonian systems. The subject material is presented from both the qualitative and the quantitative point of view, with many examples to illustrate the theory, enabling the reader to begin research after studying this book.

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The first truly up-to-date look at the theory and capabilities of nonlinear dynamical systems that take the form of feedforward neural network structures Considered one of the most important types of structures in the study of neural networks and neural-like networks, feedforward networks incorporating dynamical elements have important properties and are of use in many applications. Specializing in experiential knowledge, a neural network stores and expands its knowledge base via strikingly human routes-through a learning process and information storage involving interconnection strengths known as synaptic weights. In Nonlinear Dynamical Systems: Feedforward Neural Network Perspectives, six leading authorities describe recent contributions to the development of an analytical basis for the understanding and use of nonlinear dynamical systems of the feedforward type, especially in the areas of control, signal processing, and time series analysis. Moving from an introductory discussion of the different aspects of feedforward neural networks, the book then addresses: * Classification problems and the related problem of approximating dynamic nonlinear input-output maps * The development of robust controllers and filters * The capability of neural networks to approximate functions and dynamic systems with respect to risk-sensitive error * Segmenting a time series It then sheds light on the application of feedforward neural networks to speech processing, summarizing speech-related techniques, and reviewing feedforward neural networks from the viewpoint of fundamental design issues. An up-to-date and authoritative look at the ever-widening technical boundaries and influence of neural networks in dynamical systems, this volume is an indispensable resource for researchers in neural networks and a reference staple for libraries.

Nonlinear dynamics and chaos involves the study of apparent random happenings within a system or process. The subject has wide applications within mathematics, engineering, physics and other physical sciences. Since the bestselling first edition was published, there has been a lot of new research conducted in the area of nonlinear dynamics and chaos. * Expands on the bestselling, highly regarded first edition * A new chapter which will cover the new research in the area since first edition * Glossary of terms and a bibliography have been added * All figures and illustrations will be 'modernised' * Comprehensive and systematic account of nonlinear dynamics and chaos, still a fast-growing area of applied mathematics * Highly illustrated * Excellent introductory text, can be used for an advanced undergraduate/graduate course text

Presents a system of multivariate analysis techniques in cases where statistical data may be of different measurement levels such as nominal, ordinal or interval. It covers methods of studying the stability of these techniques, including resampling by the bootstrap and jackknife and discusses sensitivity analysis through first-order approximations. The alternating least squares algorithm is used as a general model and treated in detail for the most important special cases. Among techniques covered are correspondence analysis, principal components analysis, canonical correlation analysis and various ordination techniques. The exposition also includes historical overviews, basic theoretical results, algorithmic efficiency and applications. Emphasis is placed on graphical display and nonlinear transformation of variables is used to obtain simple displays.

Complete with valuable FORTRAN programs that help solve nondifferentiable nonlinear LtandLo.-norm estimation problems, this important reference/text extensively delineates ahistory of Lp-norm estimation. It examines the nonlinear Lp-norm estimation problem that isa viable alternative to least squares estimation problems where the underlying errordistribution is nonnormal, i.e., non-Gaussian.Nonlinear LrNorm Estimation addresses both computational and statistical aspects ofLp-norm estimation problems to bridge the gap between these two fields . . . contains 70useful illustrations ... discusses linear Lp-norm as well as nonlinear Lt, Lo., and Lp-normestimation problems . . . provides all appropriate computational algorithms and FORTRANlistings for nonlinear Lt- and Lo.-norm estimation problems . . . guides readers with clear endof-chapter notes on related topics and outstanding research publications . . . contains numericalexamples plus several practical problems .. . and shows how the data can prescribe variousapplications of Lp-norm alternatives.Nonlinear Lp-Norm Estimation is an indispensable reference for statisticians,operations researchers, numerical analysts, applied mathematicians, biometricians, andcomputer scientists, as well as a text for graduate students in statistics or computer science.

This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with the mathematical theory.Richly illustrated, and with many exercises and worked examples, this book is ideal for an introductory course at the junior/senior or first-year graduate level. It is also ideal for the scientist who has not had formal instruction in nonlinear dynamics, but who now desires to begin informal study. The prerequisites are multivariable calculus and introductory physics.