H &#x221E%x; Engineering and Amplifier Optimization

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Housheng Su, Xiaofan Wang

<p>Synchronization, consensus and flocking are ubiquitous requirements in networked systems. <b><i>Pinning Control of Complex Networked Systems</i></b> investigates these requirements by using the pinning control strategy, which aims to control the whole dynamical network with huge numbers of nodes by imposing controllers for only a fraction of the nodes. As the direct control of every node in a dynamical network with huge numbers of nodes might be impossible or unnecessary, it’s then very important to use the pinning control strategy for the synchronization of complex dynamical networks. The research on pinning control strategy in consensus and flocking of multi-agent systems can not only help us to better understand the mechanisms of natural collective phenomena, but also benefit applications in mobile sensor/robot networks. This book offers a valuable resource for researchers and engineers working in the fields of control theory and control engineering. <br> <br><b>Housheng Su</b> is an Associate Professor at the Department of Control Science and Engineering, Huazhong University of Science and Technology, China; <b>Xiaofan Wang</b> is a Professor at the Department of Automation, Shanghai Jiao Tong University, China.</p>

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Alexandre Ern, Jean-Luc Guermond

This book presents the mathematical theory of finite elements, starting from basic results on approximation theory and finite element interpolation and building up to more recent research topics, such as and Discontinuous Galerkin, subgrid viscosity stabilization, and a posteriori error estimation. The body of the text is organized into three parts plus two appendices collecting the functional analysis results used in the book. The first part develops the theoretical basis for the finite element method and emphasizes the fundamental role of inf-sup conditions. The second party addresses various applications encompassing elliptic PDE's, mixed formulations, first-order PDEs, and the time-dependent versions of these problems. The third part covers implementation issues and should provide readers with most of the practical details needed to write or understand a finite element code. Written at the graduate level, the text contains numerous examples and exercises and is intended to serve as a graduate textbook. Depending on one's interests, several reading paths can be followed, emphasizing either theoretical results, numerical algorithms, code efficiency, or applications in the engineering sciences. The book will be useful to researchers and graduate students in mathematics, computer science and engineering.

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M. Vidyasagar

Learning and Generalization provides a formal mathematical theory for addressing intuitive questions such as: How does a machine learn a new concept on the basis of examples? How can a neural network, after sufficient training, correctly predict the outcome of a previously unseen input? How much training is required to achieve a specified level of accuracy in the prediction? How can one identify the dynamical behaviour of a nonlinear control system by observing its input-output behaviour over a finite interval of time? In its successful first edition, A Theory of Learning and Generalization was the first book to treat the problem of machine learning in conjunction with the theory of empirical processes, the latter being a well-established branch of probability theory. The treatment of both topics side-by-side leads to new insights, as well as to new results in both topics. This second edition extends and improves upon this material, covering new areas including: Support vector machines. Fat-shattering dimensions and applications to neural network learning. Learning with dependent samples generated by a beta-mixing process. Connections between system identification and learning theory. Probabilistic solution of 'intractable problems' in robust control and matrix theory using randomized algorithm. Reflecting advancements in the field, solutions to some of the open problems posed in the first edition are presented, while new open problems have been added. Learning and Generalization (second edition) is essential reading for control and system theorists, neural network researchers, theoretical computer scientists and probabilist.

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Dietmar Hildenbrand

<p>The author defines “Geometric Algebra Computing” as the geometrically intuitive development of algorithms using geometric algebra with a focus on their efficient implementation, and the goal of this book is to lay the foundations for the widespread use of geometric algebra as a powerful, intuitive mathematical language for engineering applications in academia and industry. The related technology is driven by the invention of conformal geometric algebra as a 5D extension of the 4D projective geometric algebra and by the recent progress in parallel processing, and with the specific conformal geometric algebra there is a growing community in recent years applying geometric algebra to applications in computer vision, computer graphics, and robotics.</p><p><p>This book is organized into three parts: in Part I the author focuses on the mathematical foundations; in Part II he explains the interactive handling of geometric algebra; and in Part III he deals with computing technology for high-performance implementations based on geometric algebra as a domain-specific language in standard programming languages such as C++ and OpenCL. The book is written in a tutorial style and readers should gain experience with the associated freely available software packages and applications.</p><p>The book is suitable for students, engineers, and researchers in computer science, computational engineering, and mathematics.