This book is devoted to new methods of control for complex dynamical systems and deals with nonlinear control systems having several degrees of freedom, subjected to unknown disturbances, and containing uncertain parameters. Various constraints are imposed on control inputs and state variables or their combinations. The book contains an introduction to the theory of optimal control and the theory of stability of motion, and also a description of some known methods based on these theories. Major attention is given to new methods of control developed by the authors over the last 15 years. Mechanical and electromechanical systems described by nonlinear Lagrange's equations are considered. General methods are proposed for an effective construction of the required control, often in an explicit form. The book contains various techniques including the decomposition of nonlinear control systems with many degrees of freedom, piecewise linear feedback control based on Lyapunov's functions, methods which elaborate and extend the approaches of the conventional control theory, optimal control, differential games, and the theory of stability. The distinctive feature of the methods developed in the book is that the c- trols obtained satisfy the imposed constraints and steer the dynamical system to a prescribed terminal state in ?nite time. Explicit upper estimates for the time of the process are given. In all cases, the control algorithms and the estimates obtained are strictly proven.

This book, written by a leader in neural network theory in Russia, uses mathematical methods in combination with complexity theory, nonlinear dynamics and optimization. It details more than 40 years of Soviet and Russian neural network research and presents a systematized methodology of neural networks synthesis. The theory is expansive: covering not just traditional topics such as network architecture but also neural continua in function spaces as well.

In this monograph, nonequilibrium statistical mechanics is developed by means of ensemble methods on the basis of the Boltzmann equation, the generic Boltzmann equations for classical and quantum dilute gases, and a generalised Boltzmann equation for dense simple fluids. The theories are developed in forms parallel with the equilibrium Gibbs ensemble theory in a way fully consistent with the laws of thermodynamics. The generalised hydrodynamics equations are the integral part of the theory and describe the evolution of macroscopic processes in accordance with the laws of thermodynamics of systems far removed from equilibrium. Audience: This book will be of interest to researchers in the fields of statistical mechanics, condensed matter physics, gas dynamics, fluid dynamics, rheology, irreversible thermodynamics and nonequilibrium phenomena.

This monograph combines the knowledge of both the field of nonlinear dynamics and non-smooth mechanics, presenting a framework for a class of non-smooth mechanical systems using techniques from both fields. The book reviews recent developments, and opens the field to the nonlinear dynamics community. This book addresses researchers and graduate students in engineering and mathematics interested in the modelling, simulation and dynamics of non-smooth systems and nonlinear dynamics.

Despite a long history of almost 180 years stretching back to the times of Carnot and, later, Clausius and Lord Kelvin, amongst others following him, the subject of thermodynamics has not as yet seen its full maturity, in the sense that the theory of irreversible processes has remained incomplete. The works of L. Onsager, J. Meixner, I. Prigogine on the thermodyn- ics of linear irreversible processes are, in effect, the early efforts toward the desired goal of giving an adequate description of irreversible processes, but their theory is confined to near-equilibrium phenomena. The works in recent years by various research workers on the extension of the aforem- tioned thermodynamic theory of linear irreversible processes are further efforts toward the goal mentioned. The present work is another of such efforts and a contribution to the subject of generalizing the thermodyn- ics of reversible processes, namely, equilibrium thermodynamics, to that of irreversible processes-non-equilibrium thermodynamics, without being restricted to linear irreversible processes. In this context the terms 'far - moved from equilibrium' is often used in the literature, and such states of macroscopic systems and non-linear irreversible phenomena in them are the objects of interest in this work. The thermodynamics of processes, either reversible or irreversible, is a continuum mechanical theory of matter and energy and their exchange between different parts of the system, and as such it makes no direct r- erence to the molecules constituting the substance under consideration.

This monograph provides a new account of justified inference as a cognitive process. In contrast to the prevailing tradition in epistemology, the focus is on low-level inferences, i.e., those inferences that we are usually not consciously aware of and that we share with the cat nearby which infers that the bird which she sees picking grains from the dirt, is able to fly. Presumably, such inferences are not generated by explicit logical reasoning, but logical methods can be used to describe and analyze such inferences.

Part 1 gives a purely system-theoretic explication of belief and inference. Part 2 adds a reliabilist theory of justification for inference, with a qualitative notion of reliability being employed. Part 3 recalls and extends various systems of deductive and nonmonotonic logic and thereby explains the semantics of absolute and high reliability. In Part 4 it is proven that qualitative neural networks are able to draw justified deductive and nonmonotonic inferences on the basis of distributed representations. This is derived from a soundness/completeness theorem with regard to cognitive semantics of nonmonotonic reasoning. The appendix extends the theory both logically and ontologically, and relates it to A. Goldman's reliability account of justified belief.

This text will be of interest to epistemologists and logicians, to all computer scientists who work on nonmonotonic reasoning and neural networks, and to cognitive scientists.

Delay Differential Equations: Recent Advances and New Directions cohesively presents contributions from leading experts on the theory and applications of functional and delay differential equations (DDEs).

Students and researchers will benefit from a unique focus on theory, symbolic, and numerical methods, which illustrate how the concepts described can be applied to practical systems ranging from automotive engines to remote control over the Internet. Comprehensive coverage of recent advances, analytical contributions, computational techniques, and illustrative examples of the application of current results drawn from biology, physics, mechanics, and control theory.

Students, engineers and researchers from various scientific fields will find Delay Differential Equations: Recent Advances and New Directions a valuable reference.

Cellular Neural Networks (CNNs) constitute a class of nonlinear, recurrent and locally coupled arrays of identical dynamical cells that operate in parallel. ANALOG chips are being developed for use in applications where sophisticated signal processing at low power consumption is required. Signal processing via CNNs only becomes efficient if the network is implemented in analog hardware. In view of the physical limitations that analog implementations entail, robust operation of a CNN chip with respect to parameter variations has to be insured. By far not all mathematically possible CNN tasks can be carried out reliably on an analog chip; some of them are inherently too sensitive. This book defines a robustness measure to quantify the degree of robustness and proposes an exact and direct analytical design method for the synthesis of optimally robust network parameters. The method is based on a design centering technique which is generally applicable where linear constraints have to be satisfied in an optimum way. Processing speed is always crucial when discussing signal-processing devices. In the case of the CNN, it is shown that the setting time can be specified in closed analytical expressions, which permits, on the one hand, parameter optimization with respect to speed and, on the other hand, efficient numerical integration of CNNs. Interdependence between robustness and speed issues are also addressed. Another goal pursued is the unification of the theory of continuous-time and discrete-time systems. By means of a delta-operator approach, it is proven that the same network parameters can be used for both of these classes, even if their nonlinear output functions differ. More complex CNN optimization problems that cannot be solved analytically necessitate resorting to numerical methods. Among these, stochastic optimization techniques such as genetic algorithms prove their usefulness, for example in image classification problems. Since the inception of the CNN, the problem of finding the network parameters for a desired task has been regarded as a learning or training problem, and computationally expensive methods derived from standard neural networks have been applied. Furthermore, numerous useful parameter sets have been derived by intuition. In this book, a direct and exact analytical design method for the network parameters is presented. The approach yields solutions which are optimum with respect to robustness, an aspect which is crucial for successful implementation of the analog CNN hardware that has often been neglected. `This beautifully rounded work provides many interesting and useful results, for both CNN theorists and circuit designers.' Leon O. Chua

This book examines the testing and modeling of materials and structures under dynamic loading conditions. Readers get an in-depth analysis of the current mathematical modeling and simulation tools available for a variety of materials, alongside discussions of the benefits and limitations of these tools in industrial design. Following a logical and well organized structure, this volume uniquely combines experimental procedures with numerical simulation, and provides many examples.

Systemics of Emergence: Research and Development is a volume devoted to exploring the core theoretical and disciplinary research problems of emergence processes from which systems are established. It focuses on emergence as the key point of any systemic process. This topic is dealt with within different disciplinary approaches, indicated by the organization in sections: 1) Applications; 2) Biology and human care; 3) Cognitive Science; 4) Emergence; 5) General Systems; 6) Learning; 7) Management; 8) Social Systems; 9) Systemic Approach and Information Science; 10) Theoretical issues in Systemics.

The Editors and contributing authors have produced this volume to help, encourage and widen the work in this area of General Systems Research.

People have always asked what distinguishes the living from the inanimate world and what uni?es the two. The ?elds of biology and physics have a long history of exchange. Milestones at the molecular level were the discoveries of the structure ofDNA, RNA, andproteins. It is not by coincidence that this exchange has intensi?ed in recent years. Laboratory experiments reach down to the level of single molecules. Moreover, thereisnowavastamountofgenomicinformation, whichisstillgrowingex- nentially due to the various sequencing projects. Biologists increasingly feel the need for theoretical models to interpret these data in a quantitative way. At the sametime, theoreticalphysicshasmadesigni?cantprogressinareaslikelyto be relevant for the understanding of biological systems. Some important ex- plesarecooperativephenomena, statisticsfarfromthermodynamicequilibrium, systemswithquencheddisorder, andsoftmatter. Some forms of biological matter have indeed become established areas of - searchwithinphysics, suchasbiomembranes, heteropolymers, molecularmotors, microtubules, neuralsystemsetc.Thisvolumeisfocusedonadi?erentaspect of the living world that can be calledbiologicalinformation, itscoding, rep- duction, andevolution.Biologicalinformationistranslatedintostructuresand patternsoveranenormousrangeofscales, fromsinglebiomoleculestospecies networks coupled over entire continents. Thestatisticaltheory of biological information lives not only in three-dim- sional space. It involves various abstract spaces in which this information is encodedandevolves, suchasnucleotidesequences, genenetworks, ortopologies of the 'tree of life'. The articles collected highlight a few directions of research that may become important parts of this emerging ?eld. The ?rst part of the book, MolecularInformationandEvolution, startswith twoarticlesonsequencesimilarityanalysis, acentralthemeinbioinformatics which has surprisingly deep connections to statistical physics. The genetic code, RNA, andproteinsarethreeexamplesoftheintricateinterplayofsequence, structure, andfunction

This book has a long history of more than 20 years. The first attempt to write a monograph on information-theoretic approach to thermodynamics was done by one of the authors (RSI) in 1974 when he published, in the preprint form, two volumes of the book "Information Theory and Thermodynamics" concerning classical and quantum information theory, [153] (220 pp.), [154] (185 pp.). In spite of the encouraging remarks by some of the readers, the physical part of this book was never written except for the first chapter. Now this material is written completely anew and in much greater extent. A few years earlier, in 1970, second author of the present book, (AK), a doctoral student and collaborator of RSI in Toruli, published in Polish, also as a preprint, his habilitation dissertation "Information-theoretical decision scheme in quantum statistical mechanics" [196] (96 pp.). This small monograph presented his original results in the physical part of the theory developed in the Torun school. Unfortunately, this preprint was never published in English. The present book contains all these results in a much more modern and developed form.

Data Mining for Design and Manufacturing: Methods and Applications is the first book that brings together research and applications for data mining within design and manufacturing. The aim of the book is 1) to clarify the integration of data mining in engineering design and manufacturing, 2) to present a wide range of domains to which data mining can be applied, 3) to demonstrate the essential need for symbiotic collaboration of expertise in design and manufacturing, data mining, and information technology, and 4) to illustrate how to overcome central problems in design and manufacturing environments. The book also presents formal tools required to extract valuable information from design and manufacturing data, and facilitates interdisciplinary problem solving for enhanced decision making. Audience: The book is aimed at both academic and practising audiences. It can serve as a reference or textbook for senior or graduate level students in Engineering, Computer, and Management Sciences who are interested in data mining technologies. The book will be useful for practitioners interested in utilizing data mining techniques in design and manufacturing as well as for computer software developers engaged in developing data mining tools.

100 years after the first observation of ripening by Ostwald and 40 years after the first publication of a theory describing this process, this monograph presents in a self-consistent and comprehensive manner, all the bits and pieces of coarsening theories so that the main issues and the underlying mathematics of self-similar coarsening of dispersed systems can be understood. Rather than giving a complete survey of the field, it presents a careful derivation of the existing results and places them into some perspective.

This book contains the courses given at the Third School on Statistical Physics and Cooperative Systems held at Santiago, Chile, from 14th to 18th December 1992. The main idea of this periodic school was to bring together scientists work with recent trends in Statistical Physics. More precisely ing on subjects related related with non linear phenomena, dynamical systems, ergodic theory, cellular au tomata, symbolic dynamics, large deviation theory and neural networks. Scientists working in these subjects come from several areas: mathematics, biology, physics, computer science, electrical engineering and artificial intelligence. Recently, a very important cross-fertilization has taken place with regard to the aforesaid scientific and technological disciplines, so as to give a new approach to the research whose common core remains in statistical physics. Each contribution is devoted to one or more of the previous subjects. In most cases they are structured as surveys, presenting at the same time an original point of view about the topic and showing mostly new results. The expository text of Fran"

This book is the first comprehensive volume on nonlinear dynamics and chaos in optical systems. A few books have been published recently, but they summarize applied mathematical methodologies toward understanding of nonlinear dynamics in laser systems with small degrees of freedom focusing on linearized perturbation and bifurcation analyses. In contrast to these publications, this book summarizes nonlinear dynamic problems in optical complex systems possessing large degrees of freedom, systematically featuring our original experimental results and their theoretical treatments. The new concepts introduced in this book will have a wide appeal to audiences involved in a rapidly-growing field of nonlinear dynamics. This book focuses on nonlinear dynamics and cooperative functions in realistic optical complex systems, such as multimode lasers, laser array, coupled nonlinear-element systems, and their applications to optical processing. This book is prepared for graduate students majoring in optical and laser physics, but the generic nature of complex systems described in this book may stimulate researchers in the field of nonlinear dynamics covering different academic areas including applied mathematics, hydrodynamics, celestial mechanics, chemistry, biology, and economics.

The aim of this NATO ASI has been to present an up-to-date overview of current areas of interest in amorphous materials. In order to limit the material to a manageable amount, the meeting was concerned exclusively with insulating and semiconducting materials. The lectures and seminars fill the gap between graduate courses and research seminars. The lecturers and seminar speakers were chosen as experts in their respective areas and the lectures and seminars that were given are presented in this volume. During the first week of the meeting. an emphasis was placed on introductory lectures, mainly associated with questions relating to the glass-formation and the structure of glasses. The second week focused more on research seminars. Each day of the meeting. about four posters were presented during the coffee breaks, and these formed an important focus for discussions. The posters are not reproduced in this volume as the editors wanted to have only larger contributions to make this volume more coherent. This volume is organized into four sections, starting with general considerations of the glass forming ability and techniques for the preparation of different kinds of glasses.

Multi-Valued and Universal Binary Neurons deals with two new types of neurons: multi-valued neurons and universal binary neurons. These neurons are based on complex number arithmetic and are hence much more powerful than the typical neurons used in artificial neural networks. Therefore, networks with such neurons exhibit a broad functionality. They can not only realise threshold input/output maps but can also implement any arbitrary Boolean function. Two learning methods are presented whereby these networks can be trained easily. The broad applicability of these networks is proven by several case studies in different fields of application: image processing, edge detection, image enhancement, super resolution, pattern recognition, face recognition, and prediction. The book is hence partitioned into three almost equally sized parts: a mathematical study of the unique features of these new neurons, learning of networks of such neurons, and application of such neural networks. Most of this work was developed by the first two authors over a period of more than 10 years and was only available in the Russian literature. With this book we present the first comprehensive treatment of this important class of neural networks in the open Western literature. Multi-Valued and Universal Binary Neurons is intended for anyone with a scholarly interest in neural network theory, applications and learning. It will also be of interest to researchers and practitioners in the fields of image processing, pattern recognition, control and robotics.

Evolutionary algorithms, such as evolution strategies, genetic algorithms, or evolutionary programming, have found broad acceptance in the last ten years. In contrast to its broad propagation, theoretical analysis in this subject has not progressed as much. This monograph provides the framework and the first steps toward the theoretical analysis of Evolution Strategies (ES). The main emphasis is deriving a qualitative understanding of why and how these ES algorithms work.

In spite of the impressive predictive power and strong mathematical structure of quantum mechanics, the theory has always suffered from important conceptual problems. Some of these have never been solved. Motivated by this state of affairs, a number of physicists have worked together for over thirty years to develop stochastic electrodynamics, a physical theory aimed at finding a conceptually satisfactory, realistic explanation of quantum phenomena. This is the first book to present a comprehensive review of stochastic electrodynamics, from its origins to present-day developments. After a general introduction for the non-specialist, a critical discussion is presented of the main results of the theory as well as of the major problems encountered. A chapter on stochastic optics and some interesting consequences for local realism and the Bell inequalities is included. In the final chapters the authors propose and develop a new version of the theory that brings it in closer correspondence with quantum mechanics and sheds some light on the wave aspects of matter and the linkage with quantum electrodynamics. Audience: The volume will be of interest to scholars and postgraduate students of theoretical and mathematical physics, foundations and philosophy of physics, and teachers of theoretical physics and quantum mechanics, electromagnetic theory, and statistical physics (stochastic processes).

This volume is intended to be used as a textbook for a special topic course in computer science. It addresses contemporary research topics of interest such as intelligent control, genetic algorithms, neural networks, optimization techniques, expert systems, fractals, and computer vision. The work incorporates many new research ideas, and focuses on the role of continuous mathematics. Audience: This book will be valuable to graduate students interested in theoretical computer topics, algorithms, expert systems, neural networks, and software engineering.

Modern physics is confronted with a large variety of complex spatial patterns. Although both spatial statisticians and statistical physicists study random geometrical structures, there has been only little interaction between the two up to now because of different traditions and languages.
This volume aims to change this situation by presenting in a clear way fundamental concepts of spatial statistics which are of great potential value for condensed matter physics and materials sciences in general, and for porous media, percolation and Gibbs processes in particular. Geometric aspects, in particular ideas of stochastic and integral geometry, play a central role throughout. With nonspecialist researchers and graduate students also in mind, prominent physicists give an excellent introduction here to modern ideas of statistical physics pertinent to this exciting field of research.

One service mathematics has rendered the 'Et moi, ..., si j'avait Sil comment en revenir, je n'y serais point aIle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences_ Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ...'; 'One service logic has rendered com- puter science .. :; 'One service category theory has rendered mathematics ...'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Recent Advances in Reinforcement Learning addresses current research in an exciting area that is gaining a great deal of popularity in the Artificial Intelligence and Neural Network communities. Reinforcement learning has become a primary paradigm of machine learning. It applies to problems in which an agent (such as a robot, a process controller, or an information-retrieval engine) has to learn how to behave given only information about the success of its current actions. This book is a collection of important papers that address topics including the theoretical foundations of dynamic programming approaches, the role of prior knowledge, and methods for improving performance of reinforcement-learning techniques. These papers build on previous work and will form an important resource for students and researchers in the area. Recent Advances in Reinforcement Learning is an edited volume of peer-reviewed original research comprising twelve invited contributions by leading researchers. This research work has also been published as a special issue of Machine Learning (Volume 22, Numbers 1, 2 and 3).

The 24 papers presented at the international concluding colloquium of the German priority programme (DFG-Verbundschwerpunktprogramm) "Transition," held in April 2002 in Stuttgart.

The unique and successful programme ran six years, starting April 1996, and was sponsored mainly by the Deutsche Forschungsgemeinschaft, DFG, but also by the Deutsches Zentrum f r Luft-und Raumfahrt, DLR, the Physikalisch-Technische Bundesanstalt Braunschweig, PTB, and Airbus Deutschland. The papers summarise the results of the programme and cover transition mechanisms, transition prediction, transition control, natural transition and measurement techniques, transition - turbulence - separation, and visualisation issues. Three invited papers are devoted to mechanisms of turbulence production, to a general framework of stability, receptivity and control, and a forcing model for receptivity analysis. Almost every transition topic arising in subsonic and transonic flow is covered.