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Data driven identification of networks of dynamic systems
\"The identification of network connected dynamic systems is currently a hot research topic within the community of systems and control. Other engineering areas, social sciences and system biology are putting a lot of effort in the study of network connected systems. Modeling such networks and the identification of these models from acquired measurements is crucial in the analysis or understanding of the dynamics. Based on these models, synthesis to modify the behavior of the network can also be performed. This book gives a unique overview of state of the art research in the field of identifying networks of linear dynamical systems. This overview combines many of the pioneering contributions from the authors with those of other researchers that play a crucial role in the development of this new field\"-- Provided by publisher.
Book
Quantitative assessments of distributed systems : methodologies and techniques
Distributed systems employed in critical infrastructures must fulfill dependability, timeliness, and performance specifications. Since these systems most often operate in an unpredictable environment, their design and maintenance require quantitative evaluation of deterministic and probabilistic timed models. This need gave birth to an abundant literature devoted to formal modeling languages combined with analytical and simulative solution techniques The aim of the book is to provide an overview of techniques and methodologies dealing with such specific issues in the context of distributed systems and covering aspects such as performance evaluation, reliability/availability, energy efficiency, scalability, and sustainability. Specifically, techniques for checking and verifying if and how a distributed system satisfies the requirements, as well as how to properly evaluate non-functional aspects, or how to optimize the overall behavior of the system, are all discussed in the book. The scope has been selected to provide a thorough coverage on issues, models. and techniques relating to validation, evaluation and optimization of distributed systems. The key objective of this book is to help to bridge the gaps between modeling theory and the practice in distributed systems through specific examples.
eBook
Optimization for Communications and Networks
This book provides an introduction to optimization theory and its applications. It is written for senior undergraduate students and first-year graduate students of telecommunication and related fields. Most applications pertain to communication and network problems. The book has practical examples to accompany rigorous discussion so that the r
eBook
Computational network theory : theoretical foundations and applications
This comprehensive introduction to computational network theory as a branch of network theory builds on the understanding that such networks are a tool to derive or verify hypotheses by applying computational techniques to large scale network data.The highly experienced team of editors and high-profile authors from around the world present and explain a number of methods that are representative of computational network theory, derived from graph theory, as well as computational and statistical techniques. With its coherent structure and homogenous style, this reference is equally suitable for courses on computational networks.
eBook
Graph Theoretic Methods in Multiagent Networks
This accessible book provides an introduction to the analysis and design of dynamic multiagent networks. Such networks are of great interest in a wide range of areas in science and engineering, including: mobile sensor networks, distributed robotics such as formation flying and swarming, quantum networks, networked economics, biological synchronization, and social networks. Focusing on graph theoretic methods for the analysis and synthesis of dynamic multiagent networks, the book presents a powerful new formalism and set of tools for networked systems.
The book's three sections look at foundations, multiagent networks, and networks as systems. The authors give an overview of important ideas from graph theory, followed by a detailed account of the agreement protocol and its various extensions, including the behavior of the protocol over undirected, directed, switching, and random networks. They cover topics such as formation control, coverage, distributed estimation, social networks, and games over networks. And they explore intriguing aspects of viewing networks as systems, by making these networks amenable to control-theoretic analysis and automatic synthesis, by monitoring their dynamic evolution, and by examining higher-order interaction models in terms of simplicial complexes and their applications.
The book will interest graduate students working in systems and control, as well as in computer science and robotics. It will be a standard reference for researchers seeking a self-contained account of system-theoretic aspects of multiagent networks and their wide-ranging applications.
This book has been adopted as a textbook at the following universities:
University of Stuttgart, GermanyRoyal Institute of Technology, SwedenJohannes Kepler University, AustriaGeorgia Tech, USAUniversity of Washington, USAOhio University, USA
eBook
Optimization Algorithms on Matrix Manifolds
Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It places careful emphasis on both the numerical formulation of the algorithm and its differential geometric abstraction--illustrating how good algorithms draw equally from the insights of differential geometry, optimization, and numerical analysis. Two more theoretical chapters provide readers with the background in differential geometry necessary to algorithmic development. In the other chapters, several well-known optimization methods such as steepest descent and conjugate gradients are generalized to abstract manifolds. The book provides a generic development of each of these methods, building upon the material of the geometric chapters. It then guides readers through the calculations that turn these geometrically formulated methods into concrete numerical algorithms. The state-of-the-art algorithms given as examples are competitive with the best existing algorithms for a selection of eigenspace problems in numerical linear algebra. Optimization Algorithms on Matrix Manifolds offers techniques with broad applications in linear algebra, signal processing, data mining, computer vision, and statistical analysis. It can serve as a graduate-level textbook and will be of interest to applied mathematicians, engineers, and computer scientists.
eBook
Fuzzy Multi-Criteria Decision Making
In summarizing the concepts and results of the most popular fuzzy multicriteria methods, using numerical examples, this work examines all the most recently developed methods. Each one of the 22 chapters include practical applications along with new results.
eBook
Robust Optimization
Robust optimization is still a relatively new approach to optimization problems affected by uncertainty, but it has already proved so useful in real applications that it is difficult to tackle such problems today without considering this powerful methodology. Written by the principal developers of robust optimization, and describing the main achievements of a decade of research, this is the first book to provide a comprehensive and up-to-date account of the subject. Robust optimization is designed to meet some major challenges associated with uncertainty-affected optimization problems: to operate under lack of full information on the nature of uncertainty; to model the problem in a form that can be solved efficiently; and to provide guarantees about the performance of the solution. The book starts with a relatively simple treatment of uncertain linear programming, proceeding with a deep analysis of the interconnections between the construction of appropriate uncertainty sets and the classical chance constraints (probabilistic) approach. It then develops the robust optimization theory for uncertain conic quadratic and semidefinite optimization problems and dynamic (multistage) problems. The theory is supported by numerous examples and computational illustrations. An essential book for anyone working on optimization and decision making under uncertainty, Robust Optimization also makes an ideal graduate textbook on the subject.
eBook
Positive Definite Matrices
This book represents the first synthesis of the considerable body of new research into positive definite matrices. These matrices play the same role in noncommutative analysis as positive real numbers do in classical analysis. They have theoretical and computational uses across a broad spectrum of disciplines, including calculus, electrical engineering, statistics, physics, numerical analysis, quantum information theory, and geometry. Through detailed explanations and an authoritative and inspiring writing style, Rajendra Bhatia carefully develops general techniques that have wide applications in the study of such matrices. Bhatia introduces several key topics in functional analysis, operator theory, harmonic analysis, and differential geometry--all built around the central theme of positive definite matrices. He discusses positive and completely positive linear maps, and presents major theorems with simple and direct proofs. He examines matrix means and their applications, and shows how to use positive definite functions to derive operator inequalities that he and others proved in recent years. He guides the reader through the differential geometry of the manifold of positive definite matrices, and explains recent work on the geometric mean of several matrices. Positive Definite Matrices is an informative and useful reference book for mathematicians and other researchers and practitioners. The numerous exercises and notes at the end of each chapter also make it the ideal textbook for graduate-level courses.
eBook
Spectrum of the Koopman Operator, Spectral Expansions in Functional Spaces, and State-Space Geometry
We examine spectral operator-theoretic properties of linear and nonlinear dynamical systems with globally stable attractors. Using the Kato decomposition, we develop a spectral expansion for general linear autonomous dynamical systems with analytic observables and define the notion of generalized eigenfunctions of the associated Koopman operator. We interpret stable, unstable and center subspaces in terms of zero-level sets of generalized eigenfunctions. We then utilize conjugacy properties of Koopman eigenfunctions and the new notion of open eigenfunctions—defined on subsets of state space—to extend these results to nonlinear dynamical systems with an equilibrium. We provide a characterization of (global) center manifolds, center-stable, and center-unstable manifolds in terms of joint zero-level sets of families of Koopman operator eigenfunctions associated with the nonlinear system. After defining a new class of Hilbert spaces, that capture the on- and off-attractor properties of dissipative dynamics, and introducing the concept of modulated Fock spaces, we develop spectral expansions for a class of dynamical systems possessing globally stable limit cycles and limit tori, with observables that are square-integrable in on-attractor variables and analytic in off-attractor variables. We discuss definitions of stable, unstable, and global center manifolds in such nonlinear systems with (quasi)-periodic attractors in terms of zero-level sets of Koopman operator eigenfunctions. We define the notion of isostables for a general class of nonlinear systems. In contrast with the systems that have discrete Koopman operator spectrum, we provide a simple example of a measure-preserving system that is not chaotic but has continuous spectrum, and discuss experimental observations of spectrum on such systems. We also provide a brief characterization of the data types corresponding to the obtained theoretical results and define the coherent principal dimension for a class of datasets based on the lattice-type principal spectrum of the associated Koopman operator.
Journal Article