Joos P.L. Vandewalle

How does homebanking work? How are board games developed? How reliable can wind energy get? How do we discover forged paintings? Do smart girls stay single? How dangerous can a bioterrorist get? In all these questions (and many others), mathematics plays a crucial role in the search for an answer.? This book tells the story behind twenty of these questions. This is explicitly not a mathematics book, but a book about the crucial role that mathematics plays in devising the creative solutions the world needs. The questions are divided into three categories: mathematics in everyday life, mathematics for the workplace, and mathematics for tomorrow's society. The themes illustrate not only the incredibly broad applicability of mathematics in the world around us, but also the great diversity of useful mathematical techniques.

Artificial neural networks possess several properties that make them particularly attractive for applications to modelling and control of complex non-linear systems. Among these properties are their universal approximation ability, their parallel network structure and the availability of on- and off-line learning methods for the interconnection weights. However, dynamic models that contain neural network architectures might be highly non-linear and difficult to analyse as a result. Artificial Neural Networks for Modelling and Control of Non-Linear Systems investigates the subject from a system theoretical point of view. However the mathematical theory that is required from the reader is limited to matrix calculus, basic analysis, differential equations and basic linear system theory. No preliminary knowledge of neural networks is explicitly required. The book presents both classical and novel network architectures and learning algorithms for modelling and control. Topics include non-linear system identification, neural optimal control, top-down model based neural control design and stability analysis of neural control systems. A major contribution of this book is to introduce NLq Theory as an extension towards modern control theory, in order to analyze and synthesize non-linear systems that contain linear together with static non-linear operators that satisfy a sector condition: neural state space control systems are an example. Moreover, it turns out that NLq Theory is unifying with respect to many problems arising in neural networks, systems and control. Examples show that complex non-linear systems can be modelled and controlled within NLq theory, including mastering chaos. The didactic flavor of this book makes it suitable for use as a text for a course on Neural Networks. In addition, researchers and designers will find many important new techniques, in particular NLqTheory, that have applications in control theory, system theory, circuit theory and Time Series Analysis.

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

Modern industrial processes and systems require adaptable advanced control protocols able to deal with circumstances demanding "judgement” rather than simple "yes/no”, "on/off” responses: circumstances where a linguistic description is often more relevant than a cut-and-dried numerical one. The ability of fuzzy systems to handle numeric and linguistic information within a single framework renders them efficacious for this purpose. Fuzzy Logic, Identification and Predictive Control first shows you how to construct static and dynamic fuzzy models using the numerical data from a variety of real industrial systems and simulations. The second part exploits such models to design control systems employing techniques like data mining. This monograph presents a combination of fuzzy control theory and industrial serviceability that will make a telling contribution to your research whether in the academic or industrial sphere and also serves as a fine roundup of the fuzzy control area for the graduate student.

For engineering applications that are based on nonlinear phenomena, novel information processing systems require new methodologies and design principles. This perspective is the basis of the three cornerstones of this book: cellular neural networks, chaos and synchronization. Cellular neural networks and their universal machine implementations offer a well-established platform for processing spatial-temporal patterns and wave computing. Multi-scroll circuits are generalizations to the original Chua's circuit, leading to chip implementable circuits with increasingly complex attractors. Several applications make use of synchronization techniques for nonlinear systems. A systematic overview is given for Lur'e representable systems with global synchronization criteria for master-slave and mutual synchronization, robust synchronization, H8 synchronization, time-delayed systems and impulsive synchronization.

Modern industrial processes and systems require adaptable advanced control protocols able to deal with circumstances demanding "judgement” rather than simple "yes/no”, "on/off” responses: circumstances where a linguistic description is often more relevant than a cut-and-dried numerical one. The ability of fuzzy systems to handle numeric and linguistic information within a single framework renders them efficacious for this purpose. Fuzzy Logic, Identification and Predictive Control first shows you how to construct static and dynamic fuzzy models using the numerical data from a variety of real industrial systems and simulations. The second part exploits such models to design control systems employing techniques like data mining. This monograph presents a combination of fuzzy control theory and industrial serviceability that will make a telling contribution to your research whether in the academic or industrial sphere and also serves as a fine roundup of the fuzzy control area for the graduate student.

This book focuses on Least Squares Support Vector Machines (LS-SVMs) which are reformulations to standard SVMs. LS-SVMs are closely related to regularization networks and Gaussian processes but additionally emphasize and exploit primal-dual interpretations from optimization theory. The authors explain the natural links between LS-SVM classifiers and kernel Fisher discriminant analysis. Bayesian inference of LS-SVM models is discussed, together with methods for imposing sparseness and employing robust statistics. The framework is further extended towards unsupervised learning by considering PCA analysis and its kernel version as a one-class modelling problem. This leads to new primal-dual support vector machine formulations for kernel PCA and kernel CCA analysis. Furthermore, LS-SVM formulations are given for recurrent networks and control. In general, support vector machines may pose heavy computational challenges for large data sets. For this purpose, a method of fixed size LS-SVM is proposed where the estimation is done in the primal space in relation to a Nyström sampling with active selection of support vectors. The methods are illustrated with several examples.

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

Artificial neural networks possess several properties that make them particularly attractive for applications to modelling and control of complex non-linear systems. Among these properties are their universal approximation ability, their parallel network structure and the availability of on- and off-line learning methods for the interconnection weights. However, dynamic models that contain neural network architectures might be highly non-linear and difficult to analyse as a result. Artificial Neural Networks for Modelling and Control of Non-Linear Systems investigates the subject from a system theoretical point of view. However the mathematical theory that is required from the reader is limited to matrix calculus, basic analysis, differential equations and basic linear system theory. No preliminary knowledge of neural networks is explicitly required. The book presents both classical and novel network architectures and learning algorithms for modelling and control. Topics include non-linear system identification, neural optimal control, top-down model based neural control design and stability analysis of neural control systems. A major contribution of this book is to introduce NLq Theory as an extension towards modern control theory, in order to analyze and synthesize non-linear systems that contain linear together with static non-linear operators that satisfy a sector condition: neural state space control systems are an example. Moreover, it turns out that NLq Theory is unifying with respect to many problems arising in neural networks, systems and control. Examples show that complex non-linear systems can be modelled and controlled within NLq theory, including mastering chaos. The didactic flavor of this book makes it suitable for use as a text for a course on Neural Networks. In addition, researchers and designers will find many important new techniques, in particular NLqTheory, that have applications in control theory, system theory, circuit theory and Time Series Analysis.