In recent years, there has been a growing interest in applying neural networks to dynamic systems identification (modelling), prediction and control. Neural networks are computing systems characterised by the ability to learn from examples rather than having to be programmed in a conventional sense. Their use enables the behaviour of complex systems to be modelled and predicted and accurate control to be achieved through training, without a priori information about the systems' structures or parameters. This book describes examples of applications of neural networks In modelling, prediction and control. The topics covered include identification of general linear and non-linear processes, forecasting of river levels, stock market prices and currency exchange rates, and control of a time-delayed plant and a two-joint robot. These applications employ the major types of neural networks and learning algorithms. The neural network types considered in detail are the muhilayer perceptron (MLP), the Elman and Jordan networks and the Group-Method-of-Data-Handling (GMDH) network. In addition, cerebellar-model-articulation-controller (CMAC) networks and neuromorphic fuzzy logic systems are also presented. The main learning algorithm adopted in the applications is the standard backpropagation (BP) algorithm. Widrow-Hoff learning, dynamic BP and evolutionary learning are also described.

In wntmg this monograph my aim has been to present a "geometric" approach to the structural synthesis of multivariable control systems that are linear, time-invariant and of finite dynamic order. The book is ad dressed to graduate students specializing in control, to engineering scientists involved in control systems research and development, and to mathemati cians interested in systems control theory. The label "geometric" in the title is applied for several reasons. First and obviously, the setting is linear state space and the mathematics chiefly linear algebra in abstract (geometric) style. The basic ideas are the familiar system concepts of controllability and observability, thought of as geometric prop erties of distinguished state subspaces. Indeed, the geometry was first brought in out of revulsion against the orgy of matrix manipulation which linear control theory mainly consisted of, around fifteen years ago. But secondly and of greater interest, the geometric setting rather quickly sug gested new methods of attacking synthesis which have proved to be intuitive and economical; they are also easily reduced to matrix arithmetic as soon as you want to compute. The essence of the "geometric" approach is just this: instead of looking directly for a feedback law (say u = Fx) which would solve your synthesis problem if a solution exists, first characterize solvability as a verifiable property of some constructible state subspace, say Y. Then, if all is well, you may calculate F from Y quite easily."

Many developments on the cutting edge of research in operator theory and its applications are reflected in this collection of original and review articles. Particular emphasis lies on highlighting the interplay between operator theory and applications from other areas, such as multi-dimensional systems and function theory of several complex variables, distributed parameter systems and control theory, mathematical physics, wavelets, and numerical analysis.

Perspectives On Software Requirements presents perspectives on several current approaches to software requirements. Each chapter addresses a specific problem where the authors summarize their experiences and results to produce well-fit and traceable requirements. Chapters highlight familiar issues with recent results and experiences, which are accompanied by chapters describing well-tuned new methods for specific domains.

This book provides an up-to-date introduction to information theory. In addition to the classical topics discussed, it provides the first comprehensive treatment of the theory of I-Measure, network coding theory, Shannon and non-Shannon type information inequalities, and a relation between entropy and group theory. ITIP, a software package for proving information inequalities, is also included. With a large number of examples, illustrations, and original problems, this book is excellent as a textbook or reference book for a senior or graduate level course on the subject, as well as a reference for researchers in related fields.

OO It is a matter of general consensus that in the last decade the H _ optimization for robust control has dominated the research effort in control systems theory. Much attention has been paid equally to the mathematical instrumentation and the computational aspects. There are several excellent monographs that cover the standard topics in the area. Among the recent issues we have to cite here Linear Robust Control authored by Green and Limebeer (Prentice Hall 1995), Robust Controller Design Using Normalized Coprime Factor Plant Descriptions - by McFarlane and Glover (Springer Verlag 1989), Robust and Optimal Control - by Zhou, Doyle and Glover (Prentice Hall 1996). Thus, when the authors of the present monograph decided to start the work they were confronted with a very rich literature on the subject. However two reasons motivated their initiative. The first concerns the theory in which the whole development of the book was embedded. As is well known, there are several ways of approach oo ing H and robust control theory. Here we mention three relevant direc tions chronologically ordered: a) the first makes use of a generalization of the Beurling-Lax theorem to Krein spaces; b) the second makes use of a generalization of Nevanlinna-Pick interpolation theory and commutant lifting theorem; c) the third, and probably the most attractive from an el evate engineering viewpoint, is the two Riccati equations based approach which offers a complete solution in state space form."

Information Macrodynamics (IMD) belong to an interdisciplinary science that represents a new theoretical and computer-based methodology for a system informational descriptionand improvement,including various activities in such areas as thinking, intelligent processes, communications, management, and other nonphysical subjects with their mutual interactions, informational superimposition, and theinformation transferredbetweeninteractions. The IMD is based on the implementation of a single concept by a unique mathematical principle and formalism, rather than on an artificial combination of many arbitrary, auxiliary concepts and/or postulates and different mathematical subjects, such as the game, automata, catastrophe, logical operations theories, etc. This concept is explored mathematically using classical mathematics as calculus of variation and the probability theory, which are potent enough, without needing to developnew,specifiedmathematical systemicmethods. The formal IMD model automatically includes the related results from other fields, such as linear, nonlinear, collective and chaotic dynamics, stability theory, theory of information, physical analogies of classical and quantum mechanics, irreversible thermodynamics, andkinetics. The main IMD goal is to reveal the information regularities, mathematically expressed by the considered variation principle (VP), as a mathematical tool to extractthe regularities and define the model, whichdescribes theregularities. The IMD regularities and mechanisms are the results of the analytical solutions and are not retained by logical argumentation, rational introduction, and a reasonable discussion. The IMD's information computer modeling formalism includes a human being (as an observer, carrier and producer ofinformation), with a restoration of the model during the objectobservations.

Object-Oriented Computer Simulation of Discrete-Event Systems offers a comprehensive presentation of a wide repertoire of computer simulation techniques available to the modelers of dynamic systems. Unlike other books on simulation, this book includes a complete and balanced description of all essential issues relevant to computer simulation of discrete event systems, and it teaches simulation users how to design, program and exploit their own computer simulation models. In addition, it uses the object-oriented methodology throughout the book as its main programming platform. The reader is expected to have some background in the theory of probability and statistics and only a little programming experience in C++, as the book is not tied down to any particular simulation language. The book also provides 50 complete simulation problems to assist with writing such simulation programs. Object-Oriented Computer Simulation of Discrete-Event Systems demonstrates the basic and generic concepts used in computer simulation of discrete-event systems in a comprehensive, uniform and self-contained manner.

A. K. TURNER Department of Geology and Geological Engineering Colorado School of Mines Golden, Colorado 80401 USA Geology deals with three-dimensional data. Geoscientists are concerned with three dimensional spatial observations, measurements, and explanations of a great variety of phenomena. The representation of three-dimensional data has always been a problem. Prior to computers, graphical displays involved specialized maps, cross-sections, fence diagrams, and geometrical constructions such as stereonets. All were designed to portray three-dimensional relationships on two-dimensional paper products, and all were time consuming to develop. Until recently, computers were of little assistance to three-dimensional data handling and representation problems. Memory was too expensive to handle the huge amounts of data required by three-dimensional assessments; computational speeds were too slow to perform the necessary calculations within a reasonable time; and graphical displays had too Iowa resolution or were much too expensive to produce useful visualizations. Much experience was gained with two-dimensional geographic information systems (GIS), which were applied to many land-use management and resource assessment problems. The two-dimensional GIS field matured rapidly in the late 1980's and became widely accepted. The advent of the modern computer workstation, with its enhanced memory and graphical capabilities at ever more affordable prices, has largely overcome these earlier constraints.

Conceived by Count Jacopo Francesco Riccati more than a quarter of a millennium ago, the Riccati equation has been widely studied in the subsequent centuries. Since its introduction in control theory in the sixties, the matrix Riccati equation has known an impressive range of applications, such as optimal control, H? optimization and robust stabilization, stochastic realization, synthesis of linear passive networks, to name but a few. This book consists of 11 chapters surveying the main concepts and results related to the matrix Riccati equation, both in continuous and discrete time. Theory, applications and numerical algorithms are extensively presented in an expository way. As a foreword, the history and prehistory of the Riccati equation is concisely presented.

Controlled stochastic processes with discrete time form a very interest ing and meaningful field of research which attracts widespread attention. At the same time these processes are used for solving of many applied problems in the queueing theory, in mathematical economics. in the theory of controlled technical systems, etc. . In this connection, methods of the theory of controlled processes constitute the every day instrument of many specialists working in the areas mentioned. The present book is devoted to the rather new area, that is, to the optimal control theory with functional constraints. This theory is close to the theory of multicriteria optimization. The compromise between the mathematical rigor and the big number of meaningful examples makes the book attractive for professional mathematicians and for specialists who ap ply mathematical methods in different specific problems. Besides. the book contains setting of many new interesting problems for further invf'stigatioll. The book can form the basis of special courses in the theory of controlled stochastic processes for students and post-graduates specializing in the ap plied mathematics and in the control theory of complex systf'ms. The grounding of graduating students of mathematical department is sufficient for the perfect understanding of all the material. The book con tains the extensive Appendix where the necessary knowledge ill Borel spaces and in convex analysis is collected. All the meaningful examples can be also understood by readers who are not deeply grounded in mathematics.

An open process of restandardization, conducted by the IEEE, has led to the definitions of the new VHDL standard. The changes make VHDL safer, more portable, and more powerful. VHDL also becomes bigger and more complete. The canonical simulator of VHDL is enriched by new mechanisms, the predefined environment is more complete, and the syntax is more regular and flexible. Discrepancies and known bugs of VHDL'87 have been fixed. However, the new VHDL'92 is compatible with VHDL'87, with some minor exceptions. This book presents the new VHDL'92 for the VHDL designer. New features ar explained and classified. Examples are provided, each new feature is given a rationale and its impact on design methodology, and performance is analysed. Where appropriate, pitfalls and traps are explained. The VHDL designer will quickly be able to find the feature needed to evaluate the benefits it brings, to modify previous VHDL'87 code to make it more efficient, more portable, and more flexible. VHDL'92 is the essential update for all VHDL designers and managers involved in electronic design.

This book presents new approaches to constructing fuzzy models for model-based control. Simulated examples and real-world applications from chemical and process engineering illustrate the main methods and techniques. Supporting MATLAB and Simulink files create a computational platform for exploration of the concepts and algorithms.

The International Conference on Linear Statistical Inference LINSTAT'93 was held in Poznan, Poland, from May 31 to June 4, 1993. The purpose of the confer ence was to enable scientists, from various countries, engaged in the diverse areas of statistical sciences and practice to meet together and exchange views and re sults related to the current research on linear statistical inference in its broadest sense. Thus, the conference programme included sessions on estimation, prediction and testing in linear models, on robustness of some relevant statistical methods, on estimation of variance components appearing in linear models, on certain gen eralizations to nonlinear models, on design and analysis of experiments, including optimality and comparison of linear experiments, and on some other topics related to linear statistical inference. Within the various sessions 22 invited papers and 37 contributed papers were presented, 12 of them as posters. The conference gathered 94 participants from eighteen countries of Europe, North America and Asia. There were 53 participants from abroad and 41 from Poland. The conference was the second of this type, devoted to linear statistical inference. The first was held in Poznan in June, 4-8, 1984. Both belong to the series of confer ences on mathematical statistics and probability theory organized under the auspices of the Committee of Mathematics of the Polish Academy of Sciences, due to the ini tiative and efforts of its Mathematical Statistics Section. In the years 1973-1993 there were held in Poland nineteen such conferences, some of them international."

Information theory, cybernetics and the theory of finite automata are used to model learning-by-doing, bounded rationality, routine behavior, and the formation of teams. The non-neoclassical characterization of production developed in this book ignores the usual quantitative relationships between inputs and outputs and instead views production strictly as a problem of control and communication. The motivation for this unconventional characterization of production comes from Schumpeter's critique of neoclassical economic theory. Schumpeter argued that neoclassical economic theory, and the habits of thought engendered by it, was the major obstacle to acquiring an understanding of technological change. The non-neoclassical characterization of production developed in this book is in keeping with how economic historians describe specific technological changes and how they write technological histories about particular machines, firms or industries.

The aim of the book is to present the state of the art of the theory of symmetric (Hermitian) matrix Riccati equations and to contribute to the development of the theory of non-symmetric Riccati equations as well as to certain classes of coupled and generalized Riccati equations occurring in differential games and stochastic control. The volume offers a complete treatment of generalized and coupled Riccati equations. It deals with differential, discrete-time, algebraic or periodic symmetric and non-symmetric equations, with special emphasis on those equations appearing in control and systems theory. Extensions to Riccati theory allow to tackle robust control problems in a unified approach.

The book is intended to make available classical and recent results to engineers and mathematicians alike. It is accessible to graduate students in mathematics, applied mathematics, control engineering, physics or economics. Researchers working in any of the fields where Riccati equations are used can find the main results with the proper mathematical background.

"This volume is a textbook on linear control systems with an emphasis on stochastic optimal control with solution methods using spectral factorization in line with the original approach of N. Wiener. Continuous-time and discrete-time versions are presented in parallel.... Two appendices introduce functional analytic concepts and probability theory, and there are 77 references and an index. The chapters (except for the last two) end with problems.... [T]he book presents in a clear way important concepts of control theory and can be used for teaching." -Zentralblatt Math "This is a textbook intended for use in courses on linear control and filtering and estimation on (advanced) levels. Its major purpose is an introduction to both deterministic and stochastic control and estimation. Topics are treated in both continuous time and discrete time versions.... Each chapter involves problems and exercises, and the book is supplemented by appendices, where fundamentals on Hilbert and Banach spaces, operator theory, and measure theoretic probability may be found. The book will be very useful for students, but also for a variety of specialists interested in deterministic and stochastic control and filtering." -Applications of Mathematics "The strength of the book under review lies in the choice of specialized topics it contains, which may not be found in this form elsewhere. Also, the first half would make a good standard course in linear control." -Journal of the Indian Institute of Science

Robust Modal Control covers most classical multivariable modal control design techniques that were shown to be effective in practice, and in addition proposes several new tools. The proposed new tools include: minimum energy eigenvector selection, low order observer-based control design, conversion to observer-based controllers, a new multimodel design technique, and modal analysis. The text is accompanied by a CD-ROM containing MATLAB(r) software for the implementation of the proposed techniques. The software is in use in aeronautical industry and has proven to be effective and functional.
For more detail, please visit the author's webpage at http: //www.cert.fr/dcsd/idco/perso/Magni/booksandtb.html

Hidenori Kimura, renowned system and control theorist, turned 60 years of age in November, 2001. To celebrate this memorable occasion, his friends, collaborators, and former students gathered from all over the world and held a symposium in his honor on November 1 and 2, 2001, at the Sanjo Conference Hall at the University of Tokyo. Reflecting his current research interests, the symposium was entitled "Cybernetics in the 21st Century: Information and Complexity in Control Theory," and it drew nearly 150 attendees. There were twenty-five lectures, on which the present volume is based. Hidenori Kimura was born on November 3, 1941, in Tokyo, just prior to the outbreak of the Second World War. It is not hard to imagine, then, that his early days, like those of so many of his contemporaries, must have been difficult. Fortunately, the war ended in 1945, and his generation found itself thoroughly occupied with the rebuilding effort and with Japan's uphill journey in the last half-century. He entered the University of Tokyo in 1963, received a B. S. in 1965, an M. S. in 1967, and, in 1970, a Ph. D. degree for his dissertation "A Study of Differential Games. " After obtaining his doctorate, he joined the Department of Control En gineering at Osaka University as a research associate, and in 1973 he was promoted to an associate professor.

On becoming familiar with difference equations and their close re lation to differential equations, I was in hopes that the theory of difference equations could be brought completely abreast with that for ordinary differential equations. [HUGH L. TURRITTIN, My Mathematical Expectations, Springer Lecture Notes 312 (page 10), 1973] A major task of mathematics today is to harmonize the continuous and the discrete, to include them in one comprehensive mathematics, and to eliminate obscurity from both. [E. T. BELL, Men of Mathematics, Simon and Schuster, New York (page 13/14), 1937] The theory of time scales, which has recently received a lot of attention, was introduced by Stefan Hilger in his PhD thesis [159] in 1988 (supervised by Bernd Aulbach) in order to unify continuous and discrete analysis. This book is an intro duction to the study of dynamic equations on time scales. Many results concerning differential equations carryover quite easily to corresponding results for difference equations, while other results seem to be completely different in nature from their continuous counterparts. The study of dynamic equations on time scales reveals such discrepancies, and helps avoid proving results twice, once for differential equa tions and once for difference equations. The general idea is to prove a result for a dynamic equation where the domain of the unknown function is a so-called time scale, which is an arbitrary nonempty closed subset of the reals.

This practical yet rigorous book provides a development of nonlinear, Lyapunov-based tools and their use in the solution of control-theoretic problems. Rich in motivating examples and new design techniques, the text balances theoretical foundations and real-world implementation.

Saturation nonlinearities are ubiquitous in engineering systems. In control systems, every physical actuator or sensor is subject to saturation owing to its maximum and minimum limits. A digital filter is subject to saturation if it is implemented in a finite word length format. Saturation nonlinearities are also purposely introduced into engineering systems such as control sys tems and neural network systems. Regardless of how saturation arises, the analysis and design of a system that contains saturation nonlinearities is an important problem. Not only is this problem theoretically challenging, but it is also practically imperative. This book intends to study control systems with actuator saturation in a systematic way. It will also present some related results on systems with state saturation or sensor saturation. Roughly speaking, there are two strategies for dealing with actuator sat uration. The first strategy is to neglect the saturation in the first stage of the control design process, and then to add some problem-specific schemes to deal with the adverse effects caused by saturation. These schemes, known as anti-windup schemes, are typically introduced using ad hoc modifications and extensive simulations. The basic idea behind these schemes is to intro duce additional feedbacks in such a way that the actuator stays properly within its limits. Most of these schemes lead to improved performance but poorly understood stability properties."

With contributions by specialists in optimization and practitioners in the fields of aerospace engineering, chemical engineering, and fluid and solid mechanics, the major themes include an assessment of the state of the art in optimization algorithms as well as challenging applications in design and control, in the areas of process engineering and systems with partial differential equation models.

Small noise is a good noise. In this work, we are interested in the problems of estimation theory concerned with observations of the diffusion-type process Xo = Xo, 0 ~ t ~ T, (0. 1) where W is a standard Wiener process and St(') is some nonanticipative smooth t function. By the observations X = {X , 0 ~ t ~ T} of this process, we will solve some t of the problems of identification, both parametric and nonparametric. If the trend S(-) is known up to the value of some finite-dimensional parameter St(X) = St((}, X), where (} E e c Rd , then we have a parametric case. The nonparametric problems arise if we know only the degree of smoothness of the function St(X), 0 ~ t ~ T with respect to time t. It is supposed that the diffusion coefficient c is always known. In the parametric case, we describe the asymptotical properties of maximum likelihood (MLE), Bayes (BE) and minimum distance (MDE) estimators as c --+ 0 and in the nonparametric situation, we investigate some kernel-type estimators of unknown functions (say, StO,O ~ t ~ T). The asymptotic in such problems of estimation for this scheme of observations was usually considered as T --+ 00 , because this limit is a direct analog to the traditional limit (n --+ 00) in the classical mathematical statistics of i. i. d. observations. The limit c --+ 0 in (0. 1) is interesting for the following reasons.

The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge of manifolds, dynamical systems, tensors, and differential forms. Some applications to Hamiltonian mechanics, fluid me chanics, electromagnetism, plasma dynamics and control thcory arc given in Chapter 8, using both invariant and index notation. The current edition of the book does not deal with Riemannian geometry in much detail, and it does not treat Lie groups, principal bundles, or Morse theory. Some of this is planned for a subsequent edition. Meanwhile, the authors will make available to interested readers supplementary chapters on Lie Groups and Differential Topology and invite comments on the book's contents and development. Throughout the text supplementary topics are given, marked with the symbols ~ and {l:;J. This device enables the reader to skip various topics without disturbing the main flow of the text. Some of these provide additional background material intended for completeness, to minimize the necessity of consulting too many outside references. We treat finite and infinite-dimensional manifolds simultaneously. This is partly for efficiency of exposition. Without advanced applications, using manifolds of mappings, the study of infinite-dimensional manifolds can be hard to motivate.