Advances in science and technology necessitate the use of increasingly-complicated dynamic control processes. Undoubtedly, sophisticated mathematical models are also concurrently elaborated for these processes. In particular, linear dynamic control systems iJ = Ay + Bu, y E M C ]Rn, U E ]RT, (1) where A and B are constants, are often abandoned in favor of nonlinear dynamic control systems (2) which, in addition, contain a large number of equations. The solution of problems for multidimensional nonlinear control systems en counters serious difficulties, which are both mathematical and technical in nature. Therefore it is imperative to develop methods of reduction of nonlinear systems to a simpler form, for example, decomposition into systems of lesser dimension. Approaches to reduction are diverse, in particular, techniques based on approxi mation methods. In this monograph, we elaborate the most natural and obvious (in our opinion) approach, which is essentially inherent in any theory of math ematical entities, for instance, in the theory of linear spaces, theory of groups, etc. Reduction in our interpretation is based on assigning to the initial object an isomorphic object, a quotient object, and a subobject. In the theory of linear spaces, for instance, reduction consists in reducing to an isomorphic linear space, quotient space, and subspace. Strictly speaking, the exposition of any mathemat ical theory essentially begins with the introduction of these reduced objects and determination of their basic properties in relation to the initial object."

From the reviews: "The book is an excellent combination of theory and real-world applications. Each application not only demonstrates the power of the theoretical results but also is important on its own behalf." IEEE Control Systems Magazine

In this revised and expanded edition, Howard E. Jordan explains-in a clear manner-the technology of energy efficient electric motors including motor losses, testing, and efficiency labeling. He also discusses how to calculate the return on investment for an energy efficient motor in addition to several other subjects related to effective motor applications. New chapters explore permanent magnet synchronous motors and transistor pulse-width-modulated inverters. Engineers, purchasing managers, and executives who make decisions on motor selection will find this an invaluable reference.

This book focuses mainly on fractional Brownian fields and their extensions. It has been used to teach graduate students at Grenoble and Toulouse's Universities. It is as self-contained as possible and contains numerous exercises, with solutions in an appendix. After a foreword by Stephane Jaffard, a long first chapter is devoted to classical results from stochastic fields and fractal analysis. A central notion throughout this book is self-similarity, which is dealt with in a second chapter with a particular emphasis on the celebrated Gaussian self-similar fields, called fractional Brownian fields after Mandelbrot and Van Ness's seminal paper. Fundamental properties of fractional Brownian fields are then stated and proved. The second central notion of this book is the so-called local asymptotic self-similarity (in short lass), which is a local version of self-similarity, defined in the third chapter. A lengthy study is devoted to lass fields with finite variance. Among these lass fields, we find both Gaussian fields and non-Gaussian fields, called Levy fields. The Levy fields can be viewed as bridges between fractional Brownian fields and stable self-similar fields. A further key issue concerns the identification of fractional parameters. This is the raison d'etre of the statistics chapter, where generalized quadratic variations methods are mainly used for estimating fractional parameters. Last but not least, the simulation is addressed in the last chapter. Unlike the previous issues, the simulation of fractional fields is still an area of ongoing research. The algorithms presented in this chapter are efficient but do not claim to close the debate.

Counting is one of the basic elementary mathematical activities. It comes with two complementary aspects: to determine the number of elements of a set - and to create an ordering between the objects of counting just by counting them over. For finite sets of objects these two aspects are realized by the same type of num bers: the natural numbers. That these complementary aspects of the counting pro cess may need different kinds of numbers becomes apparent if one extends the process of counting to infinite sets. As general tools to determine numbers of elements the cardinals have been created in set theory, and set theorists have in parallel created the ordinals to count over any set of objects. For both types of numbers it is not only counting they are used for, it is also the strongly related process of calculation - especially addition and, derived from it, multiplication and even exponentiation - which is based upon these numbers. For fuzzy sets the idea of counting, in both aspects, looses its naive foundation: because it is to a large extent founded upon of the idea that there is a clear distinc tion between those objects which have to be counted - and those ones which have to be neglected for the particular counting process."

Evolutionary algorithms (EAs) are becoming increasingly attractive for researchers from various disciplines, such as operations research, computer science, industrial engineering, electrical engineering, social science, economics, etc. This book presents an insightful, comprehensive, and up-to-date treatment of EAs, such as genetic algorithms, differential evolution, evolution strategy, constraint optimization, multimodal optimization, multiobjective optimization, combinatorial optimization, evolvable hardware, estimation of distribution algorithms, ant colony optimization, particle swarm optimization, artificial immune systems, artificial life, genetic programming, etc.

It emphasises the initiative ideas of the algorithm, contains discussions in the contexts, and suggests further readings and possible research projects. All the methods form a pedagogical way to make EAs easy and interesting.

This textbook also introduces the applications of EAs as many as possible. At least one real-life application is introduced by the end of almost every chapter. The authors focus on the kernel part of applications, such as how to model real-life problems, how to encode and decode the individuals, how to design effective search operators according to the chromosome structures, etc.

This textbook adopts pedagogical ways of making EAs easy and interesting. Its methods include an introduction at the beginning of each chapter, emphasising the initiative, discussions in the contexts, summaries at the end of every chapter, suggested further reading, exercises, and possible research projects.

Introduction to Evolutionary Algorithms will enable students to:

establish a strong background on evolutionary algorithms;

appreciate the cutting edge of EAs;

perform their own research projects by simulating the application introduced in the book; and

apply their intuitive ideas to academic search.

This book is aimed at senior undergraduate students or first-year graduate students as a textbook or self-study material."

Simulation based on mathematical models plays a major role in computer aided design of integrated circuits (ICs). Decreasing structure sizes, increasing packing densities and driving frequencies require the use of refined mathematical models, and to take into account secondary, parasitic effects. This leads to very high dimensional problems which nowadays require simulation times too large for the short time-to-market demands in industry. Modern Model Order Reduction (MOR) techniques present a way out of this dilemma in providing surrogate models which keep the main characteristics of the device while requiring a significantly lower simulation time than the full model. With Model Reduction for Circuit Simulation we survey the state of the art in the challenging research field of MOR for ICs, and also address its future research directions. Special emphasis is taken on aspects stemming from miniturisations to the nano scale. Contributions cover complexity reduction using e.g., balanced truncation, Krylov-techniques or POD approaches. For semiconductor applications a focus is on generalising current techniques to differential-algebraic equations, on including design parameters, on preserving stability, and on including nonlinearity by means of piecewise linearisations along solution trajectories (TPWL) and interpolation techniques for nonlinear parts. Furthermore the influence of interconnects and power grids on the physical properties of the device is considered, and also top-down system design approaches in which detailed block descriptions are combined with behavioral models. Further topics consider MOR and the combination of approaches from optimisation and statistics, and the inclusion of PDE models with emphasis on MOR for the resulting partial differential algebraic systems. The methods which currently are being developed have also relevance in other application areas such as mechanical multibody systems, and systems arising in chemistry and to biology. The current number of books in the area of MOR for ICs is very limited, so that this volume helps to fill a gap in providing the state of the art material, and to stimulate further research in this area of MOR. Model Reduction for Circuit Simulation also reflects and documents the vivid interaction between three active research projects in this area, namely the EU-Marie Curie Action ToK project O-MOORE-NICE (members in Belgium, The Netherlands and Germany), the EU-Marie Curie Action RTN-project COMSON (members in The Netherlands, Italy, Germany, and Romania), and the German federal project System reduction in nano-electronics (SyreNe).

The Seventh Rochester Conference on Coherence and Quantum Optics was held on the campus of the University of Rochester during the four-day period June 7 - 10, 1996. More than 280 scientists from 33 countries participated. This book contains the Proceedings of the meeting. This Conference differed from the previous six in the series in having only a limited number of oral presentations, in order to avoid too many parallel sessions. Another new feature was the introduction of tutorial lectures. Most contributed papers were presented in poster sessions. The Conference was sponsored by the American Physical Society, by the Optical Society of America, by the International Union of Pure and Applied Physics and by the University of Rochester. We wish to express our appreciation to these organizations for their support and we especially extend our thanks to the International Union of Pure and Applied Physics for providing financial assistance to a number of speakers from Third World countries, to enable them to take part in the meeting.

Just a few years ago, virtual reality was regarded as more a toy than a tool. Today, however, it is becoming the enabling technology for man-machine communications. The rapid development of graphics hardware and soft ware makes its application possible. Besides building walkthroughs and landscape fly-overs with very realistic visual effects, we can recognize the trend toward industrial applications. This is because of the emerging need for tools for rapid product development. Especially in the aeronautical and automotive industries, companies have began to investigate and develop virtual reality tools for their own needs in co-operation with research or ganizations. In co-operation with the Fraunhofer Institute for Computer Graphics (IGD), the Computer Graphics Center (ZGDV) in Darmstadt established the German working group on virtual reality in 1993 as a forum for infor mation exchange between industry and research. German researchers, system developers, and industrial users have met several times in Darm stadt at the Computer Graphics Center. In these meetings they discussed the essential issues inherent in applying virtual reality to industrial appli cations and exchanged their latest research results and experiences.

From its early beginnings in the fifties and sixties, the field of neural networks has been steadily developing to become one of the most interdisciplinary areas of research within computer science. This volume contains a selection of papers from WIRN Vietri-99, the 11th Italian Workshop on Neural Nets. This annual event, sponsored, amongst others, by the IEEE Neural Networks Council and the INNS/SIG Italy, brings together the best of research from all over the world. The papers cover a range of topics within neural networks, including pattern recognition, signal and image processing, mathematical models, neuro-fuzzy models and economics applications.

The most powerful computers in the world are not only used for scientific research, defence, and business, but also in game playing. Computer games are a multi-billion dollar industry. Recent advances in computational intelligence paradigms have generated tremendous interest among researchers in the theory and implementation of games. Game theory is a branch of operational research dealing with decision theory in a competitive situation. Game theory involves the mathematical calculations and heuristics to optimize the efficient lines of play. This book presents a sample of the most recent research on the application of computational intelligence techniques in games. This book contains 7 chapters. The first chapter, by Chen, Fanelli, Castellano, and Jain, is an introduction to computational intelligence paradigms. It presents the basics of the main constituents of compu tational intelligence paradigms including knowledge representation, probability-based approaches, fuzzy logic, neural networks, genetic algorithms, and rough sets. In the second chapter, Chellapilla and Fogel present the evolution of a neural network to play checkers without human expertise. This chapter focuses on the use of a population of neural networks, where each network serves as an evaluation function to describe the quality of the current board position. After only a little more than 800 generations, the evolutionary process has generated a neural network that can play checkers at the expert level as designated by the u.s. Chess Federation rating system. The program developed by the authors has also competed well against commercially available software."

Control of Discrete-event Systems provides a survey of the most important topics in the discrete-event systems theory with particular focus on finite-state automata, Petri nets and max-plus algebra. Coverage ranges from introductory material on the basic notions and definitions of discrete-event systems to more recent results. Special attention is given to results on supervisory control, state estimation and fault diagnosis of both centralized and distributed/decentralized systems developed in the framework of the Distributed Supervisory Control of Large Plants (DISC) project. Later parts of the text are devoted to the study of congested systems though fluidization, an over approximation allowing a much more efficient study of observation and control problems of timed Petri nets. Finally, the max-plus algebraic approach to the analysis and control of choice-free systems is also considered. Control of Discrete-event Systems provides an introduction to discrete-event systems for readers that are not familiar with this class of systems, but also provides an introduction to research problems and open issues of current interest to readers already familiar with them. Most of the material in this book has been presented during a Ph.D. school held in Cagliari, Italy, in June 2011.

The aim of this Book is to give an overview, based on the results of nearly three decades of intensive research, of transient chaos. One belief that motivates us to write this book is that, transient chaos may not have been appreciated even within the nonlinear-science community, let alone other scientific disciplines.

Nonlinear Dynamics represents a wide interdisciplinary area of research dealing with a variety of "unusual" physical phenomena by means of nonlinear differential equations, discrete mappings, and related mathematical algorithms. However, with no real substitute for the linear superposition principle, the methods of Nonlinear Dynamics appeared to be very diverse, individual and technically complicated. This book makes an attempt to find a common ground for nonlinear dynamic analyses based on the existence of strongly nonlinear but quite simple counterparts to the linear models and tools. It is shown that, since the subgroup of rotations, harmonic oscillators, and the conventional complex analysis generate linear and weakly nonlinear approaches, then translations and reflections, impact oscillators, and hyperbolic (Clifford's) algebras must give rise to some "quasi impact" methodology. Such strongly nonlinear methods are developed in several chapters of this book based on the idea of non-smooth time substitutions. Although most of the illustrations are based on mechanical oscillators, the area of applications may include also electric, electro-mechanical, electrochemical and other physical models generating strongly anharmonic temporal signals or spatial distributions. Possible applications to periodic elastic structures with non-smooth or discontinuous characteristics are outlined in the final chapter of the book.

Resources should be used sparingly both from a point of view of economy and eco logy. Thus in controlling industrial, economical and social processes, optimization is the tool of choice. In this area of applied numerical analysis, the INTERNATIONAL FEDERATION OF AUTOMATIC CONTROL (IFAC) acts as a link between research groups in universities, national research laboratories and industry. For this pur pose, the technical committee Mathematics of Control of IFAC organizes biennial conferences with the objective of bringing together experts to exchange ideas, ex periences and future developments in control applications of optimization. There should be a genuine feedback loop between mathematicians, computer scientists, engineers and software developers. This loop should include the design, application and implementation of algorithms. The contributions of industrial practitioners are especially important. These proceedings contain selected papers from a workshop on CONTROL Ap PLICATIONS OF OPTIMIZATION, which took place at the Fachhochschule Miinchen in September 1992. The workshop was the ninth in a series of very successful bien nial meetings, starting with the Joint Automatic Control Conference in Denver in 1978 and followed by conferences in London, Oberpfaffenhofen, San Francisco, Ca pri, Tbilisi and Paris. The workshop was attended by ninety researchers from four continents. This volume represents the state of the art in the field, with emphasis on progress made since the publication of the proceedings of the Capri meeting, edited by G. di Pillo under the title 'Control Applications of Optimization and Nonlinear Programming'."

This book collects some recent works on the application of dynamic game and control theory to the analysis of environmental problems. This collec tion of papers is not the outcome of a conference or of a workshop. It is rather the result of a careful screening from among a number of contribu tions that we have solicited across the world. In particular, we have been able to attract the work of some of the most prominent scholars in the field of dynamic analyses of the environment. Engineers, mathematicians and economists provide their views and analytical tools to better interpret the interactions between economic and environmental phenomena, thus achiev ing, through this interdisciplinary effort, new and interesting results. The goal of the book is more normative than descriptive. All papers include careful modelling of the dynamics of the main variables involved in the game between nature and economic agents and among economic agents themselves, as well-described in Vrieze's introductory chapter. Fur thermore, all papers use this careful modelling framework to provide policy prescriptions to the public agencies authorized to regulate emission dy namics. Several diverse problems are addressed: from global issues, such as the greenhouse effect or deforestation, to international ones, such as the management of fisheries, to local ones, for example, the control of effluent discharges. Moreover, pollution problems are not the only concern of this book."

The craft of designing mathematical models of dynamic objects offers a large number of methods to solve subproblems in the design, typically parameter estimation, order determination, validation, model reduc tion, analysis of identifiability, sensi tivi ty and accuracy. There is also a substantial amount of process identification software available. A typi cal 'identification package' consists of program modules that implement selections of solution methods, coordinated by supervising programs, communication, and presentation handling file administration, operator of results. It is to be run 'interactively', typically on a designer's 'work station' . However, it is generally not obvious how to do that. Using interactive identification packages necessarily leaves to the user to decide on quite a number of specifications, including which model structure to use, which subproblems to be solved in each particular case, and in what or der. The designer is faced with the task of setting up cases on the work station, based on apriori knowledge about the actual physical object, the experiment conditions, and the purpose of the identification. In doing so, he/she will have to cope with two basic difficulties: 1) The com puter will be unable to solve most of the tentative identification cases, so the latter will first have to be form11lated in a way the computer can handle, and, worse, 2) even in cases where the computer can actually produce a model, the latter will not necessarily be valid for the intended purpose."

* Recommended by T.Basar, SC series ed. * This text addresses a new, active area of research and fills a gap in the literature. * Bridges mathematics, engineering, and computer science; considers stochastic and optimization aspects of congestion control in Internet data transfers. * Useful as a supplementary text & reference for grad students with some background in control theory; also suitable for researchers.

Our understanding of information and information dynamics has outgrown classical information theory. The theory does not account for the value or influence of information within the context of a system or network and does not explain how these properties might influence how information flows though and interacts with a system. The invited chapters in this collection present new theories, methods, and applications that address some of these limitations.

Dynamics of Information Systems presents state-of-the-art research explaining the importance of information in the evolution of a distributed or networked system. This book presents techniques for measuring the value or significance of information within the context of a system. Each chapter reveals a unique topic or perspective from experts in this exciting area of research.

These newly developed techniques have numerous applications including: the detection of terrorist networks, the design of highly functioning businesses and computer systems, modeling the distributed sensory and control physiology of animals, quantum entanglement and genome modeling, multi-robotic systems design, as well as industrial and manufacturing safety.

Invoking the machinery of Control Theory to control a real-world plant means, on the basis of available a priori knowledge of the plant, design ing/selecting a feasible controller accomplishing the control objective. A priori knowledge about the plant is normally represented as a mathemat ical model, given by physical laws or measurement data. Such a model is inevitably uncertain, due to measurement errors, simplified models of natural laws, neglected dynamics, and the desire to get a model tractable for further computations. Control of Uncertain Systems is therefore an im portant issue, both practically and philosophically. Basically, two different approaches exist: Adaptive Control and Robust Control. On four beautiful summer days in June 1989, researchers from 12 coun tries gathered together in Bremen, West Germany, for a workshop devoted to these issues. 49 talks, invited and contributed, were presented. The present work collects 18 of these talks. (Program and original abstracts from the workshop are available as Report 209, Institute for Dynamical System.) The papers represent a broad scope of current trends in robust and adaptive control. Topics covered include: New directions in adaptive control, stability analysis of uncertain systems, robust and adaptive stabi lization, numerical methods, and topological aspects of robust control. The papers were carefully refereed and we would like to thank the referees for their efforts, which have resulted in substantial improvements."

Integrity and Internal Control in Information Systems is a state-of-the-art book that establishes the basis for an ongoing dialogue between the IT security specialists and the internal control specialists so that both may work more effectively together to assist in creating effective business systems in the future. Building on the issues presented in the preceding volume of this series, this book seeks further answers to the following questions: What precisely do business managers need in order to have confidence in the integrity of their information systems and their data? What is the status quo of research and development in this area? Where are the gaps between business needs on the one hand and research/development on the other; what needs to be done to bridge these gaps? Integrity and Internal Control in Information Systems contains the selected proceedings of the Second Working Conference on Integrity and Internal Control in Information Systems, sponsored by the International Federation for Information Processing (IFIP) and held in Warrenton, Virginia, USA, in November 1998. It will be essential reading for academics and practitioners in computer science, information technology, business informatics, accountancy and edp-auditing.

Over recent years, a considerable amount of effort has been devoted, both in industry and academia, towards the performance modelling, evaluation and prediction of Asynchronous Transfer Mode (ATM) networks. This book describes recent advances in ATM networks reflecting the state-of-the-art technology and research achievements worldwide. In addition, it provides a fundamental source of reference in the ATM field. Research topics discussed in detail include: * Traffic Modelling and Characterisation; * Routing; * Switch and Multiplexer Models; * Call Admission Control (CAC); * Congestion Control; * Resource Allocation; * Quality of Service (QoS); * Tools and Techniques. This volume contains recently extended refereed papers of the 5th International Workshop on Performance Modelling and Evaluation of ATM Networks, which was sponsored by the International Federation for Information Processing (IFIP) and held in Ilkley, UK in July 1997.Performance Analysis of ATM Networks continues the tradition established by the first three IFIP volumes on the subject, and it is ideal for personnel in computer/communication industries as well as academic and research staff in computer science and electrical engineering.

rd This book constitutes a collection of extended versions of papers presented at the 23 IFIP TC7 Conference on System Modeling and Optimization, which was held in C- cow, Poland, on July 23-27, 2007. It contains 7 plenary and 22 contributed articles, the latter selected via a peer reviewing process. Most of the papers are concerned with optimization and optimal control. Some of them deal with practical issues, e. g. , p- formance-based design for seismic risk reduction, or evolutionary optimization in structural engineering. Many contributions concern optimization of infini- dimensional systems, ranging from a general overview of the variational analysis, through optimization and sensitivity analysis of PDE systems, to optimal control of neutral systems. A significant group of papers is devoted to shape analysis and opti- zation. Sufficient optimality conditions for ODE problems, and stochastic control methods applied to mathematical finance, are also investigated. The remaining papers are on mathematical programming, modeling, and information technology. The conference was the 23rd event in the series of such meetings biennially org- ized under the auspices of the Seventh Technical Committee "Systems Modeling and Optimization" of the International Federation for Information Processing (IFIP TC7).

One of the major contemporary challenges in both physical and social sciences is modeling, analyzing, and understanding the self-organization, evolution, behavior, and eventual decay of complex dynamical systems ranging from cell assemblies to the human brain to animal societies. The multi-faceted problems in this domain require a wide range of methods from various scienti?c disciplines. There is no question that the inclusion of time delays in complex system models considerably enriches the challenges presented by the problems. Although this inclusion often becomes inevitable as real-world applications demand more and more realistic m- els, the role of time delays in the context of complex systems so far has not attracted the interest it deserves. The present volume is an attempt toward ?lling this gap. There exist various useful tools for the study of complex time-delay systems. At the forefront is the mathematical theory of delay equations, a relatively mature ?eld in many aspects, which provides some powerful techniques for analytical inquiries, along with some other tools from statistical physics, graph theory, computer science, dynamical systems theory, probability theory, simulation and optimization software, and so on. Nevertheless, the use of these methods requires a certain synergy to address complex systems problems, especially in the presence of time delays.

Cybernetic pioneer Warren McCullough asked: "What is a man, that he may know a number; and what is a number, that a man may know it?" Thinking along much the same lines, my question here is: "What is a creative mind, that it might emerge from a complex system; and what is a complex system, that it might give rise to a creative mind?" Complexity science is a fashionable topic these days. My perspective on complexity, however, is a somewhat unusual one: I am interested in complex systems science principally as it reflects on abstract mathematical, computational models of mind. In my three previous books, The Structure of Intelligence, Evolving Mind, and Chaotic Logic, I have outlined a comprehensive complex-systems-theoretic theory of mind that I now call the psynet model. This book is a continuation of the research program presented in my previous books (and those books will be frequently referred to here, by the nicknames EM and CL). One might summarize the trajectory of thought spanning these four books as follows. SI formulated a philosophy and mathem- ics of mind, based on theoretical computer science and the concept of "pattern. " EM analyzed the theory of evolution by natural selection in similar terms, and used this computational theory of evolution to establish the evolutionary nature of thought.