1. MOTIVATION In many physical situations, a plant model is often provided with a qualitative or quantitative measure of associated model uncertainties. On the one hand, the validity of the model is guaranteed only inside a frequency band, so that nearly nothing can be said about the behavior of the real plant at high frequencies. On the other hand, if the model is derived on the basis of physical equations, it can be parameterized as a function of a few physical parameters, which are usually not perfectly known in practice. This is e.g. the case in aeronautical systems: as an example, the ae- dynamic model of an airplane is derived from the flight mechanics eq- tions. When synthesizing the aircraft control law, it is then necessary to take into account uncertainties in the values of the stability derivatives, which correspond to the physical coefficients of the aerodynamic model. Moreover, this airplane model does not perfectly represent the be- vior of the real aircraft. As a simple example, the flight control system or the autopilot are usually synthesized just using the aerodynamic model, thus without accounting for the flexible mechanicalstructure: the c- responding dynamics are indeed considered as high frequency neglected 1 dynamics, with respect to the dynamics of the rigid model .

System Modelling and Optimization covers research issues within systems theory, optimization, modelling, and computing. It includes contributions to structural mechanics, integer programming, nonlinear programming, interior point methods, dynamical systems, stability analysis, stochastic optimization, bilevel optimization, and semidefinite programming. Several survey papers written by leading experts in their fields complement new developments in theory and applications. This book contains most of the invited papers and a few carefully selected submitted papers that were presented at the 19th IFIP TC7 Conference on System Modelling and Optimization, which was held in Cambridge, England, from July 12 to 16, 1999, and sponsored by the International Federation for Information Processing (IFIP).

This book presents the latest information on both the theory and applications of networks, especially from the fields of transportation and communication, economics and human knowledge handling. It demonstrates that networks are of broad interest and that networks analysis from different disciplines offer unifying insight. Special attention is paid to networks in the ever increasing integration of Europe. Another point of focus is upon combinatorial aspects and the interactive effects between different networks, often known as synergetics.

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Chapter 3 Flexible Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . 61 3. 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3. 2 Flexible Unipolar Sigmoid Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3. 3 Flexible Bipolar Sigmoid Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3. 4 Learning Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3. 4. 1 Generalized learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 3. 4. 2 Specialized learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3. 5 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3. 6 Combinations of Flexible Artificial Neural Network Topologies . . . . 79 3. 7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Chapter 4 Self-Tuning PID Control 85 4. 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 4. 2 PID Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 4. 3 Flexible Neural Network as an Indirect Controller . . . . . . . . . . . . . . . 91 4. 4 Self-tunig PID Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4. 5 Simulation Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 4. 5. 1 The Tank model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 4. 5. 2 Simulation study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 4. 5. 3 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 4. 6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Chapter 5 Self-Tuning Computed Torque Control: Part I 107 5. 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 5. 2 Manipulator Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 5. 3 Computed Torque Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 5. 4 Self-tunig Computed Torque Control . . . . . . . . . . . . . . . . . . . . . . . . . 111 5. 5 Simulation Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 5. 5. 1 Simultaneous learning of connection weights and SF para- ters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 5. 5. 2 Learning of the sigmoid function parameters . . . . . . . . . . . . . 123 Vll 5. 5. 3 Simultaneous learning of SF parameters and output gains 129 5. 6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 Chapter 6 Self-Tuning Computed Torque Control: Part II 137 6. 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 6. 2 Simplification of Flexible Neural Networks . . . . . . . . . . . . . . . . . . . . 138 6. 3 Simulation Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 6. 3. 1 Simultaneous learning of connection weights and sigmoid function parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Pierre-Francois Verhulst, with his seminal work using the logistic map to describe population growth and saturation, paved the way for the many applications of this tool in modern mathematics, physics, chemistry, biology, economics and sociology. Indeed nowadays the logistic map is considered a useful and paradigmatic showcase for the route leading to chaos. This volume gathers contributions from some of the leading specialists in the field to present a state-of-the art view of the many ramifications of the developments initiated by Verhulst over a century ago.

The aim of this book is to advocate and promote network models of linguistic systems that are both based on thorough mathematical models and substantiated in terms of linguistics. In this way, the book contributes first steps towards establishing a statistical network theory as a theoretical basis of linguistic network analysis the boarder of the natural sciences and the humanities. This book addresses researchers who want to get familiar with theoretical developments, computational models and their empirical evaluation in the field of complex linguistic networks. It is intended to all those who are interested in statistical models of linguistic systems from the point of view of network research. This includes all relevant areas of linguistics ranging from phonological, morphological and lexical networks on the one hand and syntactic, semantic and pragmatic networks on the other. In this sense, the volume concerns readers from many disciplines such as physics, linguistics, computer science and information science. It may also be of interest for the upcoming area of systems biology with which the chapters collected here share the view on systems from the point of view of network analysis.

A predictive control algorithm uses a model of the controlled system to predict the system behavior for various input scenarios and determines the most appropriate inputs accordingly. Predictive controllers are suitable for a wide range of systems; therefore, their advantages are especially evident when dealing with relatively complex systems, such as nonlinear, constrained, hybrid, multivariate systems etc. However, designing a predictive control strategy for a complex system is generally a difficult task, because all relevant dynamical phenomena have to be considered. Establishing a suitable model of the system is an essential part of predictive control design. Classic modeling and identification approaches based on linear-systems theory are generally inappropriate for complex systems; hence, models that are able to appropriately consider complex dynamical properties have to be employed in a predictive control algorithm. This book first introduces some modeling frameworks, which can encompass the most frequently encountered complex dynamical phenomena and are practically applicable in the proposed predictive control approaches. Furthermore, unsupervised learning methods that can be used for complex-system identification are treated. Finally, several useful predictive control algorithms for complex systems are proposed and their particular advantages and drawbacks are discussed. The presented modeling, identification and control approaches are complemented by illustrative examples. The book is aimed towards researches and postgraduate students interested in modeling, identification and control, as well as towards control engineers needing practically usable advanced control methods for complex systems.

This book reports on the latest findings concerning nonlinear control theory and applications. It presents novel work on several kinds of commonly encountered nonlinear time-delay systems, including those whose nonlinear terms satisfy high-order polynomial form or general nonlinear form, those with nonlinear input or a triangular structure, and so on. As such, the book will be of interest to university researchers, R&D engineers and graduate students in the fields of control theory and control engineering who wish to learn about the core principles, methods, algorithms, and applications of nonlinear time-delay systems.

Within a conceptual framework that is developed in the two first chapters, the actual application of systems thinking is described across a broad field of cases representing research, teaching, decision support and construction. All cases are presented by experts who have actually been involved in the activities they describe. Thus, the broad selection of cases captures the great variation of systems thinking and how it is integrated into models and theories and solid knowledge pertaining to different substantive areas. At the same time all case study authors address the same set of questions that are developed in the conceptual chapters. This gives comparability across cases - chapters - and brings cohesion to the book. The focus on Sweden, an advanced country in systems thinking, reinforces the unitary context in which comparison can be made between a systems approach for better research (theory), better practice and better design and construction.

Most recent literature on systems thinking has a general (often philosophical) perspective, concerns computer systems or focuses on one highly specific problem. A special feature of this book is that, while it concerns a single nation, it simultaneously contains a broad overview of systems analysis in a number of important issue areas, for research as well as practice, against a penetrating background description of what systems analysis is, how it functions, what problems it represents and what results it may produce.

The book is intended for a broad readership and can be appreciated by experts on systems thinking and analysis as well as by students, teachers, researchers, planners and policy makers who want to learn more aboutthis topic. The book should be useful in university teaching in several disciplines.

This book is devoted to a domain of highest industrial and scienti?c interest, the complexity. The complexity understanding and management will be a main source of e?ciency and prosperity for the next decades. Complex systems areassembliesof multiple subsystemsand arecharact- ized by emergent behavior that results by nonlinear interactions among the subsystems at multiple levels of organization. Evolvability that is the ability to evolve is the method to confront and surpass the successive boundaries of complexity. Evolvability is not biological but should be considered here in the sense that the corresponding systems have, at di?erent levels, charact- istics that are naturally associated to the living systems. The signi?cance of the complexity and the phenomena of emergence are highlighted in the ?rst chapterofthe book.Theimplicationofconcepts aslevelofreality, circularity and closure for evolvable systems is evaluated. The second chapter of the book exposes the methodology to analyze and manage complex systems. The polystochastic models, PSMs, are the cons- ered mathematical tools. PSMs characterize systems emerging when several stochastic processes occurring at di?erent conditioning levels, are capable to interact with each other, resulting in qualitatively new processes and s- tems. Innovative are the higher categories approach and the introduction of apartialdi?erentialmodelfor multiple levelsmodeling.This imposes making use of appropriate notions of time, space, probabilities and entropy. Categorytheoryistheformalismcapabletooutlinethegeneralframework, shared by the functional organization of biological organisms, of cognitive systems, by the operational structure of evolvable technologies and devices and after all by the scienti?c and engineering methods

The book covers the latest theoretical results and sophisticated applications in the field of variable-structure systems and sliding-mode control. This book is divided into four parts. Part I discusses new higher-order sliding-mode algorithms, including new homogeneous controllers and differentiators. Part II then explores properties of continuous sliding-mode algorithms, such as saturated feedback control, reaching time, and orbital stability. Part III is focused on the usage of variable-structure systems (VSS) controllers for solving other control problems, for example unmatched disturbances. Finally, Part IV discusses applications of VSS; these include applications within power electronics and vehicle platooning. Variable-structure Systems and Sliding-Mode Control will be of interest to academic researchers, students and practising engineers.

This book shows how, by rather simple models, we can gain remarkable insights into the behavior of complex systems. It is devoted to the discussion of functional self-organization in large populations of interacting active elements. The possible forms of self-organization in such systems range from coherent collective motions in the physical coordinate space to the mutual synchronization of internal dynamics, the development of coherently operating groups, the rise of hierarchical structures, and the emergence of dynamical networks. Such processes play an important role in biological and social phenomena. The authors have chosen a series of models from physics, biochemistry, biology, sociology and economics, and will systematically discuss their general properties. The book addresses researchers and graduate students in a variety of disciplines, such as physics, chemistry, biology and the social sciences.

Ambient intelligence is the vision of a technology that will become invisibly embedded in our natural surroundings, present whenever we need it, enabled by simple and effortless interactions, attuned to all our senses, adaptive to users and context-sensitive, and autonomous. High-quality information access and personalized content must be available to everybody, anywhere, and at any time. This book addresses ambient intelligence used to support human contacts and accompany an individual's path through the complicated modern world. From the technical standpoint, distributed electronic intelligence is addressed as hardware vanishing into the background. Devices used for ambient intelligence are small, low-power, low weight, and (very importantly) low-cost; they collaborate or interact with each other; and they are redundant and error-tolerant. This means that the failure of one device will not cause failure of the whole system. Since wired connections often do not exist, radio methods will play an important role for data transfer. This book addresses various aspects of ambient intelligence, from applications that are imminent since they use essentially existing technologies, to ambitious ideas whose realization is still far away, due to major unsolved technical challenges.

This book showcases a subclass of hereditary systems, that is, systems with behaviour depending not only on their current state but also on their past history; it is an introduction to the mathematical theory of optimal control for stochastic difference Volterra equations of neutral type. As such, it will be of much interest to researchers interested in modelling processes in physics, mechanics, automatic regulation, economics and finance, biology, sociology and medicine for all of which such equations are very popular tools. The text deals with problems of optimal control such as meeting given performance criteria, and stabilization, extending them to neutral stochastic difference Volterra equations. In particular, it contrasts the difference analogues of solutions to optimal control and optimal estimation problems for stochastic integral Volterra equations with optimal solutions for corresponding problems in stochastic difference Volterra equations. Optimal Control of Stochastic Difference Volterra Equations commences with an historical introduction to the emergence of this type of equation with some additional mathematical preliminaries. It then deals with the necessary conditions for optimality in the control of the equations and constructs a feedback control scheme. The approximation of stochastic quasilinear Volterra equations with quadratic performance functionals is then considered. Optimal stabilization is discussed and the filtering problem formulated. Finally, two methods of solving the optimal control problem for partly observable linear stochastic processes, also with quadratic performance functionals, are developed. Integrating the author's own research within the context of the current state-of-the-art of research in difference equations, hereditary systems theory and optimal control, this book is addressed to specialists in mathematical optimal control theory and to graduate students in pure and applied mathematics and control engineering.

This monograph presents a tactical planning approach for service network design in metropolitan areas. Designing the service network requires the suitable aggregation of demand data as well as the anticipation of operational relocation decisions. To this end, an integrated approach of data analysis and mathematical optimization is introduced. The book also includes a case study based on real-world data to demonstrate the benefit of the proposed service network design approach. The target audience comprises primarily research experts in the field of traffic engineering, but the book may also be beneficial for graduate students.

This book, written by an international team of experts, introduces the reader to various aspects of complexity theory and its applications. It illustrates the latest trends in science to go beyond the mechanistic Newtonian view of the world by shifting the focus to self-organization, adaptation, and emergent phenomena. The authors discuss these properties of complex systems in biology, ecology and chemistry along with the structure and interconnectedness of the "layers" of complexity. The qualitative description is complemented by a discussion of methods for complexity quantification. Networks are covered in detail as a universal language of the complex world.

General readers, as well as undergraduate and graduate students and researchers in life sciences, chemistry, and nanotechnology will find this book to be of great interest.

This course-based text revisits classic concepts in nonlinear circuit theory from a very much introductory point of view: the presentation is completely self-contained and does not assume any prior knowledge of circuit theory. It is simply assumed that readers have taken a first-year undergraduate course in differential and integral calculus, along with an elementary physics course in classical mechanics and electrodynamics. Further, it discusses topics not typically found in standard textbooks, such as nonlinear operational amplifier circuits, nonlinear chaotic circuits and memristor networks. Each chapter includes a set of illustrative and worked examples, along with end-of-chapter exercises and lab exercises using the QUCS open-source circuit simulator. Solutions and other material are provided on the YouTube channel created for this book by the authors.

Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, interdisciplinary quality of the insights gained in the last few decades has spawned myriad applications in almost all branches of science and technology-and even well beyond. Wherever quantitative modeling and analysis of complex, nonlinear phenomena is required, chaos theory and its methods can play a key role. his fourth volume concentrates on reviewing further relevant contemporary applications of chaotic and nonlinear dynamics as they apply to the various cuttingedge branches of science and engineering. This encompasses, but is not limited to, topics such as synchronization in complex networks and chaotic circuits, time series analysis, ecological and biological patterns, stochastic control theory and vibrations in mechanical systems. Featuring contributions from active and leading research groups, this collection is ideal both as a reference and as a 'recipe book' full of tried and tested, successful engineering applications.

This book is an intellectually stimulating excursion into mathematical machines and structures capable for a universal computation. World top experts in computer science and mathematics overview exciting and intriguing topics of logical theory of monoids, geometry of Gauss word, philosophy of mathematics in computer science, asynchronous and parallel P-systems, decidability in cellular automata, splicing systems, reversible Turing machines, information flows in two-way finite automata, prime generators in automaton arrays, Grossone and Turing machines, automaton models of atomic lattices. The book is full of visually attractive examples of mathematical machines, open problems and challenges for future research. Those interested in the advancement of a theory of computation, philosophy of mathematics, future and emergent computing paradigms, architectures and implementations will find the book vital for their research and development.

Multilevel decision theory arises to resolve the contradiction between increasing requirements towards the process of design, synthesis, control and management of complex systems and the limitation of the power of technical, control, computer and other executive devices, which have to perform actions and to satisfy requirements in real time. This theory rises suggestions how to replace the centralised management of the system by hierarchical co-ordination of sub-processes. All sub-processes have lower dimensions, which support easier management and decision making. But the sub-processes are interconnected and they influence each other. Multilevel systems theory supports two main methodological tools: decomposition and co-ordination. Both have been developed, and implemented in practical applications concerning design, control and management of complex systems. In general, it is always beneficial to find the best or optimal solution in processes of system design, control and management. The real tendency towards the best (optimal) decision requires to present all activities in the form of a definition and then the solution of an appropriate optimization problem. Every optimization process needs the mathematical definition and solution of a well stated optimization problem. These problems belong to two classes: static optimization and dynamic optimization. Static optimization problems are solved applying methods of mathematical programming: conditional and unconditional optimization. Dynamic optimization problems are solved by methods of variation calculus: Euler Lagrange method; maximum principle; dynamical programming."

Using the O.D.D. (Overview, Design concepts, Detail) protocol, this title explores the role of agent-based modeling in predicting the feasibility of various approaches to sustainability. The chapters incorporated in this volume consist of real case studies to illustrate the utility of agent-based modeling and complexity theory in discovering a path to more efficient and sustainable lifestyles. The topics covered within include: households' attitudes toward recycling, designing decision trees for representing sustainable behaviors, negotiation-based parking allocation, auction-based traffic signal control, and others. This selection of papers will be of interest to social scientists who wish to learn more about agent-based modeling as well as experts in the field of agent-based modeling.

This book summarizes a network of interrelated ideas which I have developed, off and on, over the past eight or ten years. The underlying theme is the psychological interplay of order and chaos. Or, to put it another way, the interplay of deduction and induction. I will try to explain the relationship between logical, orderly, conscious, rule-following reason and fluid, self organizing, habit-governed, unconscious, chaos-infused intuition. My previous two books, The Structure of Intelligence and The Evolving Mind, briefly touched on this relationship. But these books were primarily concerned with other matters: SI with constructing a formal language for discussing mentality and its mechanization, and EM with exploring the role of evolution in thought. They danced around the edges of the order/chaos problem, without ever fully entering into it. My goal in writing this book was to go directly to the core of mental process, "where angels fear to tread" -- to tackle all the sticky issues which it is considered prudent to avoid: the nature of consciousness, the relation between mind and reality, the justification of belief systems, the connection between creativity and mental illness, .... All of these issues are dealt with here in a straightforward and unified way, using a combination of concepts from my previous work with ideas from chaos theory and complex systems science."

The book introduces novel algorithms for designing fault-tolerant control (FTC) systems using the behavioral system theoretic approach, and presents a demonstration of successful novel FTC mechanisms on several benchmark examples. The authors also discuss a new transient management scheme, which is an essential requirement for the implementation of active FTC systems, and two data-driven methodologies that are broadly classified as active FTC systems: the projection-based approach and the online-redesign approach. These algorithms do not require much a priori information about the plant in real-time, and in addition this novel implementation of active FTC systems circumvents various weaknesses induced by using a diagnostic module in real-time. The book provides graduate students taking masters and doctoral courses in mathematics, control, and electrical engineering an excellent stepping-stone for their research. It also appeals to practitioners interested to apply innovative fail-safe control techniques.

Structurally Constrained Controllers: Analysis and Synthesis studies the control of interconnected systems with a particular application in network, power systems, flight formations, etc. It introduces four important problems regarding the control of such systems and then proposes proper techniques for solving them.

This qualitative multi-case study of academic literacy is the first research to assume the premises of the Multiliteracies Project of the New London Group of literacy researchers. It takes a multimodal view of literacy, not limited to reading and writing, and sets about to uncover the Design (the flexible structuring of rules and principles) that students and teachers both follow and create in college courses. This Design takes the form of a game in which students channel content from sources, such as texts and lectures, to assessments of various kinds. Students are then rewarded in the form of grades to the extent that the content they display matches the criteria the professor sets up.

The students in this study had to determine which content would or would not match these criteria, which of six "types of information" (facts, concepts, connections, processes, principles, or metainformation, e.g., rhetorical patterns) were desired and how best to supply them. To move content from source to target they used four "operations." These include exposure (making themselves conscious of the information), extraction (a process of selecting information), manipulation (changing or synthesizing information), and display (showing the information). Greater awareness of this Design led to greater success. Pedagogical implications of this model include establishing a more realistic curricula for academic literacy programs and educating professors to better match grading criteria with learning goals.