This book provides readers to the vision of Society 5.0, which was originally proposed in the fifth Basic Science and Technology Plan by Japan's government for a technology-based, human-centered society, emerging from the 4th industrial revolution (Industry 4.0). The implementation of AI and other modern techniques in a smart society requires automated data scheduling and analysis using smart applications, a smart infrastructure, smart systems, and a smart network. Features Provides an overview of basic concepts of Society 5.0 as well as the main pillars that supports the implementation of Society 5.0. Contains the most recent research analysis in the domain of computer vision, signal processing and computing sciences for facilitating the smart homes, buildings, transport, facilities, environmental conditions and cities, and the benefits these offer to a nation. Presents the readers with practical approaches of using AI and other algorithms for smart ecosystem to deals with human dynamics, the social objects, and their relations. Deals with the utilization of AI tools and other modern techniques for smart society as well as the current challenging issues and its solutions for transformation to Society 5.0. This book is aimed at graduate and post graduate students, researchers, academicians working in the field of computer science, artificial intelligence, and machine learning.

Due to the rapid increase in readily available computing power, a corre sponding increase in the complexity of problems being tackled has occurred in the field of systems as a whole. A plethora of new methods which can be used on the problems has also arisen with a constant desire to deal with more and more difficult applications. Unfortunately by increasing the ac curacy in models employed along with the use of appropriate algorithms with related features, the resultant necessary computations can often be of very high dimension. This brings with it a whole new breed of problem which has come to be known as "The Curse of Dimensionality" . The expression "Curse of Dimensionality" can be in fact traced back to Richard Bellman in the 1960's. However, it is only in the last few years that it has taken on a widespread practical significance although the term di mensionality does not have a unique precise meaning and is being used in a slightly different way in the context of algorithmic and stochastic complex ity theory or in every day engineering. In principle the dimensionality of a problem depends on three factors: on the engineering system (subject), on the concrete task to be solved and on the available resources. A system is of high dimension if it contains a lot of elements/variables and/or the rela tionship/connection between the elements/variables is complicated."

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.

The creation of intelligent robots is surely one of the most exciting and ch- lenginggoals of Arti?cial Intelligence. A robot is, ?rst of all, nothing but an inanimate machine with motors and sensors. In order to bring life to it, the machine needs to be programmed so as to make active use of its hardware c- ponents. This turns a machine into an autonomous robot. Since about the mid nineties of the past century, robot programming has made impressive progress. State-of-the-art robots are able to orient themselves and move around freely in indoor environments or negotiate di?cult outdoor terrains, they can use stereo vision to recognize objects, and they are capable of simple object manipulation with the help of arti?cial extremities. At a time where robots perform these tasks more and more reliably, weare ready to pursue the next big step, which is to turn autonomous machines into reasoning robots.Areasoning robot exhibits higher cognitive capabilities like following complex and long-term strategies, making rational decisions on a high level, drawing logical conclusions from sensor information acquired over time, devising suitable plans, and reacting sensibly in unexpected situations. All of these capabilities are characteristics of human-like intelligence and ultimately distinguish truly intelligent robots from mere autonomous machines

This book presents the select proceedings of the International Conference on Recent Advances in Manufacturing (RAM 2020). This volume, in particular, provides insights into current research trends and opportunities within the manufacturing processes domain such as conventional and unconventional manufacturing, micro and nano manufacturing, chemical and biochemical manufacturing, and computer-integrated manufacturing (CIM). The topics covered include emerging areas of the fourth industrial revolution such as additive manufacturing, sustainable and energy-efficient manufacturing, smart manufacturing, artificial intelligence in manufacturing application, and computer-integrated manufacturing. This book will be useful for to researchers and practitioners alike.

Precision Nanometrology describes the new field of precision nanometrology, which plays an important part in nanoscale manufacturing of semiconductors, optical elements, precision parts and similar items. It pays particular attention to the measurement of surface forms of precision workpieces and to stage motions of precision machines. The first half of the book is dedicated to the description of optical sensors for the measurement of angle and displacement, which are fundamental quantities for precision nanometrology. The second half presents a number of scanning-type measuring systems for surface forms and stage motions. The systems discussed include: * error separation algorithms and systems for measurement of straightness and roundness, * the measurement of micro-aspherics, * systems based on scanning probe microscopy, and * scanning image-sensor systems. Precision Nanometrology presents the fundamental and practical technologies of precision nanometrology with a helpful selection of algorithms, instruments and experimental data. It will be beneficial for researchers, engineers and postgraduate students involved in precision engineering, nanotechnology and manufacturing.

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.

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Directs the attention to the smart digital healthcare system in this COVID-19 pandemic. Simulates novel investigations and how they will be beneficial in understanding the pandemic. Presents the latest ideas developed for data scientists, doctors, engineers, and economists. Analyses the various issues related to computing, AI apps, big data analytic techniques, and predictive scientific skill gaps. Explains some interesting and diverse types of challenges and data-driven healthcare applications.

Service orientation is emerging nowadays at multiple organizational levels in enterprise business, and it leverages technology in response to the growing need for greater business integration, flexibility and agility of manufacturing enterprises.

The "Service Oriented Architecture" (SOA) analysed throughout the book represents a technical architecture, a business modelling concept, a type of infrastructure, an integration source and a new way of viewing units of automation within the enterprise. The primary goal of SOA is to align the "business world" with the world of "information technology" in a way that makes both more effective.

The service value creation model at enterprise level consists of using a Service Component Architecture for business process applications, based on entities which handle services. In this view a service is a piece of software encapsulating the business/control logic or resource functionality of an enterprise entity that exhibits an individual competence and responds to a specific request to fulfil a local (operation) or global objective (batch production). The value creation model is based on a 2-stage approach:

"Agentification" complex manufacturing processes are split in services provided by informational agents which are discovered, accessed and executed. This leads to a modular, reusable, agile and easy integrate integration.

"Holonification" holons link the material flow and physical entities of the manufacturing processes with the informational part (IT services realized by distributed intelligence) facilitating thus traceability the developing of flexible control systems.

This book gathers contributions from scientists, researchers and industrialists on concepts, methods, frameworks and implementing issues addressing trends in the "service orientation" of control technology and management applied to manufacturing enterprise.

This book gathers contributions from scientists, researchers and industrialists on concepts, methods, frameworks and implementing issues addressing trends in the "service orientation" of control technology and management applied to manufacturing enterprise. "

Adaptive Control provides techniques for the automatic adjustment in real time of controller parameters. Their purpose is to achieve or maintain a desired level of system performance when process parameters are unknown or variable. Such techniques operate by extracting significative information from real data in order to tune the controller and they feature a mechanism for adjusting parameters. The book explores both established ideas and recent trends in the field of adaptive control. More specifically, the book covers synthesis and analysis of parameter adaptation algorithms, robust digital control and recursive digital control in open and closed loop. This book considers the problems and seeks to find answers using mathematical sequences.To guide the reader, the book contains various applications of adaptive control techniques.

The series Advances in Industrial Control aims to report and encourage technology transfer in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. New theory, new controllers, actuators, sensors, new industrial processes, computer methods, new applications, new philosophies ..., new challenges. Much of this development work resides in industrial reports, feasibility study papers and the reports of advanced collaborative projects. The series offers an opportunity for researchers to present an extended exposition of such new work in all aspects of industrial control for wider and rapid dissemination. The water and wastewater industry has undergone many changes in recent years. Of particular importance has been a renewed emphasis on improving resource management with tighter regulatory controls setting new targets on pricing, industry efficiency and loss reduction for both water and wastewater with more stringent environmental discharge conditions for wastewater. Meantime, the demand for water and wastewater services grows as the population increases and wishes for improved living conditions involving, among other items, domestic appliances that use water. Consequently, the installed infrastructure of the industry has to be continuously upgraded and extended, and employed more effectively to accommodate the new demands, both in throughput and in meeting the new regulatory conditions. Investment in fixed infrastructure is capital-intensive and slow to come on-stream. One outcome of these changes and demands is that the industry is examining the potential benefits of, and in many cases using, more advanced control systems.

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.

Congestion Control in Data Transmission Networks details the modeling and control of data traffic in communication networks. It shows how various networking phenomena can be represented in a consistent mathematical framework suitable for rigorous formal analysis. The monograph differentiates between fluid-flow continuous-time traffic models, discrete-time processes with constant sampling rates, and sampled-data systems with variable discretization periods.
The authors address a number of difficult real-life problems, such as:
optimal control of flows with disparate, time-varying delay;
the existence of source and channel nonlinearities;
the balancing of quality of service and fairness requirements; and
the incorporation of variable rate allocation policies.
Appropriate control mechanisms which can handle congestion and guarantee high throughput in various traffic scenarios (with different networking phenomena being considered) are proposed. Systematic design procedures using sound control-theoretic foundations are adopted. Since robustness issues are of major concern in providing efficient data-flow regulation in today s networks, sliding-mode control is selected as the principal technique to be applied in creating the control solutions. The controller derivation is given extensive analytical treatment and is supported with numerous realistic simulations. A comparison with existing solutions is also provided. The concepts applied are discussed in a number of illustrative examples, and supported by many figures, tables, and graphs walking the reader through the ideas and introducing their relevance in real networks.
Academic researchers and graduate students working in computer networks and telecommunications and in control (especially time-delay systems and discrete-time optimal and sliding-mode control) will find this text a valuable assistance in ensuring smooth data-flow within communications networks."

This book provides an overview of the current research in the interdisciplinary area of personal assistants (PA) and cognitively inspired systems. It discusses the most relevant topics in this highly diversified domain, like reasoning, health, personalization, robotics, and ethical and social issues. Personal assistants (PA) are a relatively new concept directed at people with cognitive or physical disabilities, and is expanding to include complex platforms such as sensors, actuators, monitoring abilities and decision processes. Designed for a general audience, it is also of interest to undergraduates, graduates and researchers involved with intelligent systems, ambient intelligence or ambient assisted living. The content goes from an introduction of the field (aimed at undergraduates and a general readership) to specific and complex architectures (aimed at graduates and researchers).

AI Metaheuristics for Information Security in Digital Media examines the latest developments in AI-based metaheuristics algorithms with applications in information security for digital media. It highlights the importance of several security parameters, their analysis, and validations for different practical applications. Drawing on multidisciplinary research including computer vision, machine learning, artificial intelligence, modified/newly developed metaheuristics algorithms, it will enhance information security for society. It includes state-of-the-art research with illustrations and exercises throughout.

Robotics is at the cusp of dramatic transformation. Increasingly complex robots with unprecedented autonomy are finding new applications, from medical surgery, to construction, to home services. Against this background, the algorithmic foundations of robotics are becoming more crucial than ever, in order to build robots that are fast, safe, reliable, and adaptive. Algorithms enable robots to perceive, plan, control, and learn. The design and analysis of robot algorithms raise new fundamental questions that span computer science, electrical engineering, mechanical engineering, and mathematics. These algorithms are also finding applications beyond robotics, for example, in modeling molecular motion and creating digital characters for video games and architectural simulation. The Workshop on Algorithmic Foundations of Robotics (WAFR) is a highly selective meeting of leading researchers in the field of robot algorithms. Since its creation in 1994, it has published some of the field's most important and lasting contributions. This book contains the proceedings of the 9th WAFR, held on December 13-15, 2010 at the National University of Singapore. The 24 papers included in this book span a wide variety of topics from new theoretical insights to novel applications.

A systematic computer-aided approach provides a versatile setting for the control engineer to overcome the complications of controller design for highly nonlinear systems. Computer-aided Nonlinear Control System Design provides such an approach based on the use of describing functions. The text deals with a large class of nonlinear systems without restrictions on the system order, the number of inputs and/or outputs or the number, type or arrangement of nonlinear terms. The strongly software-oriented methods detailed facilitate fulfillment of tight performance requirements and help the designer to think in purely nonlinear terms, avoiding the expedient of linearization which can impose substantial and unrealistic model limitations and drive up the cost of the final product. Design procedures are presented in a step-by-step algorithmic format each step being a functional unit with outputs that drive the other steps. This procedure may be easily implemented on a digital computer with example problems from mechatronic and aerospace design being used to demonstrate the techniques discussed. The author's commercial MATLAB (R)-based environment, available separately from insert URL here, can be used to create simulations showing the results of using the computer-aided control system design ideas characterized in the text. Academic researchers and graduate students studying nonlinear control systems and control engineers dealing with nonlinear plant, particularly mechatronic or aerospace systems will find Computer-aided Nonlinear Control System Design to be of great practical assistance adding to their toolbox of techniques for dealing with system nonlinearities. A basic knowledge of calculus, nonlinear analysis and software engineering will enable the reader to get the best from this book.

Inverse problems and optimal design have come of age as a consequence of the availability of better, more accurate, and more efficient simulation packages. Many of these simulators, which can run on small workstations, can capture the complicated behavior of the physical systems they are modeling, and have become commonplace tools in engineering and science. There is a great desire to use them as part of a process by which measured field data are analyzed or by which design of a product is automated. A major obstacle in doing precisely this is that one is ultimately confronted with a large-scale optimization problem. This volume contains expository articles on both inverse problems and design problems formulated as optimization. Each paper describes the physical problem in some detail and is meant to be accessible to researchers in optimization as well as those who work in applied areas where optimization is a key tool. What emerges in the presentations is that there are features about the problem that must be taken into account in posing the objective function, and in choosing an optimization strategy. In particular there are certain structures peculiar to the problems that deserve special treatment, and there is ample opportunity for parallel computation. THIS IS BACK COVER TEXT Inverse problems and optimal design have come of age as a consequence of the availability of better, more accurate, and more efficient, simulation packages. The problem of determining the parameters of a physical system from

The International Workshop on Human-Friendly Robotics (HFR) is an annual meeting that brings together academic scientists, researchers and research scholars to exchange and share their experiences and research results on all aspects related to the introduction of robots into everyday life. HFR collects contributions on current developments of a new generation of human-friendly robots, i.e., safe and dependable machines, operating in the close vicinity to humans or directly interacting with them in a wide range of domains. The papers contained in the book describe the newest and most original achievements in the field of human-robot-interaction coming from the work and ideas of young researchers. The contributions cover a wide range of topics related to human-robot interaction, both physical and cognitive, including theories, methodologies, technologies, empirical and experimental studies.

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.

"Control Performance Management in Industrial Automation "provides a coherent and self-contained treatment of a group of methods and applications of burgeoning importance to the detection and solution of problems with control loops that are vital in maintaining product quality, operational safety, and efficiency of material and energy consumption in the process industries. The monograph deals with all aspects of control performance management (CPM), from controller assessment (minimum-variance-control-based and advanced methods), to detection and diagnosis of control loop problems (process non-linearities, oscillations, actuator faults), to the improvement of control performance (maintenance, re-design of loop components, automatic controller re-tuning). It provides a contribution towards the development and application of completely self-contained and automatic methodologies in the field. Moreover, within this work, many CPM tools have been developed that goes far beyond available CPM packages.

"Control Performance Management in Industrial Automation"

. presents a comprehensive review of control performance assessment methods;

. develops methods and procedures for the detection and diagnosis of the root-causes of poor performance in complex control loops;

. covers important issues that arise when applying these assessment and diagnosis methods;

. recommends new approaches and techniques for the optimization of control loop performance based on the results of the control performance stage; and

. offers illustrative examples and industrial case studies drawn from chemicals, building, mining, pulp and paper, mineral and metal processing industries.

This book will be of interest to academic and industrial staff working on control systems design, maintenance or optimisation in all process industries."

This book discusses the supervision of hybrid systems and presents models for control, optimization and storage. It provides a guide for practitioners as well as graduate and postgraduate students and researchers in both renewable energy and modern power systems, enabling them to quickly gain an understanding of stand-alone and grid-connected hybrid renewable systems. The book is accompanied by an online MATLAB package, which offers examples of each application to help readers understand and evaluate the performance of the various hybrid renewable systems cited. With a focus on the different configurations of hybrid renewable energy systems, it offers those involved in the field of renewable energy solutions vital insights into the control, optimization and supervision strategies for the different renewable energy systems.

This book provides comprehensive coverage on a new direction in computational mathematics research: automatic search for formulas. Formulas must be sought in all areas of science and life: these are the laws of the universe, the macro and micro world, fundamental physics, engineering, weather and natural disasters forecasting; the search for new laws in economics, politics, sociology. Accumulating many years of experience in the development and application of numerical methods of symbolic regression to solving control problems, the authors offer new possibilities not only in the field of control automation, but also in the design of completely different optimal structures in many fields. For specialists in the field of control, Machine Learning Control by Symbolic Regression opens up a new promising direction of research and acquaints scientists with the methods of automatic construction of control systems.For specialists in the field of machine learning, the book opens up a new, much broader direction than neural networks: methods of symbolic regression. This book makes it easy to master this new area in machine learning and apply this approach everywhere neural networks are used. For mathematicians, the book opens up a new approach to the construction of numerical methods for obtaining analytical solutions to unsolvable problems; for example, numerical analytical solutions of algebraic equations, differential equations, non-trivial integrals, etc. For specialists in the field of artificial intelligence, the book offers a machine way to solve problems, framed in the form of analytical relationships.

The solution of eigenvalue problems is an integral part of many scientific computations. For example, the numerical solution of problems in structural dynamics, electrical networks, macro-economics, quantum chemistry, and c- trol theory often requires solving eigenvalue problems. The coefficient matrix of the eigenvalue problem may be small to medium sized and dense, or large and sparse (containing many zeroelements). In the past tremendous advances have been achieved in the solution methods for symmetric eigenvalue pr- lems. The state of the art for nonsymmetric problems is not so advanced; nonsymmetric eigenvalue problems can be hopelessly difficult to solve in some situations due, for example, to poor conditioning. Good numerical algorithms for nonsymmetric eigenvalue problems also tend to be far more complex than their symmetric counterparts. This book deals with methods for solving a special nonsymmetric eig- value problem; the symplectic eigenvalue problem. The symplectic eigenvalue problem is helpful, e.g., in analyzing a number of different questions that arise in linear control theory for discrete-time systems. Certain quadratic eigenvalue problems arising, e.g., in finite element discretization in structural analysis, in acoustic simulation of poro-elastic materials, or in the elastic deformation of anisotropic materials can also lead to symplectic eigenvalue problems. The problem appears in other applications as well.