Kybernetik og systemteori

We will occasionally footnote a portion of text with a "e;**,, to indicate Notes on the that this portion can be initially bypassed. The reasons for bypassing a Text portion of the text include: the subject is a special topic that will not be referenced later, the material can be skipped on first reading, or the level of mathematics is higher than the rest of the text. In cases where a topic is self-contained, we opt to collect the material into an appendix that can be read by students at their leisure. The material in the text cannot be fully assimilated until one makes it Notes on "e;their own"e; by applying the material to specific problems. Self-discovery Problems is the best teacher and although they are no substitute for an inquiring mind, problems that explore the subject from different viewpoints can often help the student to think about the material in a uniquely per- sonal way. With this in mind, we have made problems an integral part of this work and have attempted to make them interesting as well as informative.

Scale is a concept the antiquity of which can hardly be traced. Certainly the familiar phenomena that accompany sc ale changes in optical patterns are mentioned in the earliest written records. The most obvious topological changes such as the creation or annihilation of details have been a topic to philosophers, artists and later scientists. This appears to of fascination be the case for all cultures from which extensive written records exist. For th instance, chinese 17 c artist manuals remark that "e;distant faces have no eyes"e; . The merging of details is also obvious to many authors, e. g. , Lucretius mentions the fact that distant islands look like a single one. The one topo- logical event that is (to the best of my knowledge) mentioned only late (by th John Ruskin in his "e;Elements of drawing"e; of the mid 19 c) is the splitting of a blob on blurring. The change of images on a gradual increase of resolu- tion has been a recurring theme in the arts (e. g. , the poetic description of the distant armada in Calderon's The Constant Prince) and this "e;mystery"e; (as Ruskin calls it) is constantly exploited by painters.

Complex systems are ubiquitous, and practically all branches of science ranging from physics through chemistry and biology to economics and sociology have to deal with them. In this book we wish to present concepts and methods for dealing with complex systems from a unifying point of view. Therefore it may be of inter- est to graduate students, professors and research workers who are concerned with theoretical work in the above-mentioned fields. The basic idea for our unified ap- proach sterns from that of synergetics. In order to find unifying principles we shall focus our attention on those situations where a complex system changes its macroscopic behavior qualitatively, or in other words, where it changes its macroscopic spatial, temporal or functional structure. Until now, the theory of synergetics has usually begun with a microscopic or mesoscopic description of a complex system. In this book we present an approach which starts out from macroscopic data. In particular we shall treat systems that acquire their new structure without specific interference from the outside; i. e. systems which are self-organizing. The vehicle we shall use is information. Since this word has several quite different meanings, all of which are important for our purpose, we shall discuss its various aspects. These range from Shannon information, from which all semantics has been exorcised, to the effects of information on receivers and the self-creation of meaning.

In science, engineering and economics, decision problems are frequently modelled by optimizing the value of a (primary) objective function under stated feasibility constraints. In many cases of practical relevance, the optimization problem structure does not warrant the global optimality of local solutions; hence, it is natural to search for the globally best solution(s). Global Optimization in Action provides a comprehensive discussion of adaptive partition strategies to solve global optimization problems under very general structural requirements. A unified approach to numerous known algorithms makes possible straightforward generalizations and extensions, leading to efficient computer-based implementations. A considerable part of the book is devoted to applications, including some generic problems from numerical analysis, and several case studies in environmental systems analysis and management. The book is essentially self-contained and is based on the author's research, in cooperation (on applications) with a number of colleagues. Audience: Professors, students, researchers and other professionals in the fields of operations research, management science, industrial and applied mathematics, computer science, engineering, economics and the environmental sciences.

It has been suggested that the big questions of science are answered ¿ that science has entered a ¿twilight age¿ where all the important knowledge is known and only the details need mopping up. And yet, the unprecedented progress in science and technology in the twentieth century has raised qu- tions that weren¿t conceived of a century ago. This book argues that, far from being nearlycomplete, the storyof sciencehas many morechapters,yet unwritten. With the perspective of the century¿s advance, it¿s as if we have climbed a mountain and can see just how much broader the story is. Instead of asking how an apple falls from a tree, as Isaac Newton did in the17thcentury,wecannowask:Whatisthefundamentalnatureofanapple (matter)? How does an apple (biological organism) form and grow? Whence came the breeze that blew it loose (meteorology)? What in a physical sense (synaptic ?rings) was the idea that Newton had, and how did it form? A new approach to science that can answer such questions has sprung up in the past 30 years. This approach ¿ known as nonlinear science¿ismore than a new ?eld. Put simply, it is the recognition that throughout nature, the whole is greater than the sum of the parts. Unexpected things happen.

Model reduction and coarse-graining are important in many areas of science and engineering. How does a system with many degrees of freedom become one with fewer? How can a reversible micro-description be adapted to the dissipative macroscopic model? These crucial questions, as well as many other related problems, are discussed in this book. Specific areas of study include dynamical systems, non-equilibrium statistical mechanics, kinetic theory, hydrodynamics and mechanics of continuous media, (bio)chemical kinetics, nonlinear dynamics, nonlinear control, nonlinear estimation, and particulate systems from various branches of engineering. The generic nature and the power of the pertinent conceptual, analytical and computational frameworks helps eliminate some of the traditional language barriers, which often unnecessarily impede scientific progress and the interaction of researchers between disciplines such as physics, chemistry, biology, applied mathematics and engineering. All contributions are authored by experts, whose specialities span a wide range of fields within science and engineering.

This book is based on a two-semester course in ordinary di?erential eq- tions that I have taught to graduate students for two decades at the U- versity of Missouri. The scope of the narrative evolved over time from an embryonic collection of supplementary notes, through many classroom tested revisions, to a treatment of the subject that is suitable for a year (or more) of graduate study. If it is true that students of di?erential equations giveaway their point of viewbythewaytheydenotethederivativewith respecttotheindependent variable, then the initiated reader can turn to Chapter 1, note that I write x ?,not x , and thus correctly deduce that this book is written with an eye toward dynamical systems. Indeed, this book contains a thorough int- duction to the basic properties of di?erential equations that are needed to approach the modern theory of (nonlinear) dynamical systems. However, this is not the whole story. The book is also a product of my desire to demonstrate to my students that di?erential equations is the least insular of mathematical subjects, that it is strongly connected to almost all areas of mathematics, and it is an essential element of applied mathematics.

Linear stochastic systems are successfully used to provide mathematical models for real processes in fields such as aerospace engineering, communications, manufacturing, finance and economy. This monograph presents a useful methodology for the control of such stochastic systems with a focus on robust stabilization in the mean square, linear quadratic control, the disturbance attenuation problem, and robust stabilization with respect to dynamic and parametric uncertainty. Systems with both multiplicative white noise and Markovian jumping are covered.Key Features:-Covers the necessary pre-requisites from probability theory, stochastic processes, stochastic integrals and stochastic differential equations-Includes detailed treatment of the fundamental properties of stochastic systems subjected both to multiplicative white noise and to jump Markovian perturbations-Systematic presentation leads the reader in a natural way to the original results-New theoretical results accompanied by detailed numerical examples-Proposes new numerical algorithms to solve coupled matrix algebraic Riccati equations.The unique monograph is geared to researchers and graduate students in advanced control engineering, applied mathematics, mathematical systems theory and finance. It is also accessible to undergraduate students with a fundamental knowledge in the theory of stochastic systems.

This work brings together previously unpublished notes contributed by participants of the IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence (Moscow, 25-30 August 2006). The study of vortex motion is of great interest to fluid and gas dynamics: since all real flows are vortical in nature, applications of the vortex theory are extremely diverse, many of them (e.g. aircraft dynamics, atmospheric and ocean phenomena) being especially important.

Applications of Neural Networks gives a detailed description of 13 practical applications of neural networks, selected because the tasks performed by the neural networks are real and significant. The contributions are from leading researchers in neural networks and, as a whole, provide a balanced coverage across a range of application areas and algorithms. The book is divided into three sections. Section A is an introduction to neural networks for nonspecialists. Section B looks at examples of applications using `Supervised Training'. Section C presents a number of examples of `Unsupervised Training'. For neural network enthusiasts and interested, open-minded sceptics. The book leads the latter through the fundamentals into a convincing and varied series of neural success stories -- described carefully and honestly without over-claiming. Applications of Neural Networks is essential reading for all researchers and designers who are tasked with using neural networks in real life applications.