Download or read book Domain of Attraction written by Graziano Chesi and published by Springer Science & Business Media. This book was released on 2011-08-21 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: For nonlinear dynamical systems, which represent the majority of real devices, any study of stability requires the investigation of the domain of attraction of an equilibrium point, i.e. the set of initial conditions from which the trajectory of the system converges to equilibrium. Unfortunately, both estimating and attempting to control the domain of attraction are very difficult problems, because of the complex relationship of this set with the model of the system. Domain of Attraction addresses the estimation and control of the domain of attraction of equilibrium points via SOS programming, i.e. optimization techniques based on the sum of squares of polynomials (SOS) that have been recently developed and that amount to solving convex problems with linear matrix inequality constraints. A unified framework for addressing these issues is presented for in various cases depending on the nature of the nonlinear systems considered, including the cases of polynomial, non-polynomial, certain and uncertain systems. The methods proposed are illustrated various example systems such as electric circuits, mechanical devices, and nuclear plants. Domain of Attraction also deals with related problems that can be considered within the proposed framework, such as characterizing the equilibrium points and bounding the trajectories of nonlinear systems, and offers a concise and simple description of the main features of SOS programming, which can be used for general purpose in research and teaching.
Download or read book Domain of Attraction written by Graziano Chesi and published by Springer. This book was released on 2011-08-31 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: For nonlinear dynamical systems, which represent the majority of real devices, any study of stability requires the investigation of the domain of attraction of an equilibrium point, i.e. the set of initial conditions from which the trajectory of the system converges to equilibrium. Unfortunately, both estimating and attempting to control the domain of attraction are very difficult problems, because of the complex relationship of this set with the model of the system. Domain of Attraction addresses the estimation and control of the domain of attraction of equilibrium points via SOS programming, i.e. optimization techniques based on the sum of squares of polynomials (SOS) that have been recently developed and that amount to solving convex problems with linear matrix inequality constraints. A unified framework for addressing these issues is presented for in various cases depending on the nature of the nonlinear systems considered, including the cases of polynomial, non-polynomial, certain and uncertain systems. The methods proposed are illustrated various example systems such as electric circuits, mechanical devices, and nuclear plants. Domain of Attraction also deals with related problems that can be considered within the proposed framework, such as characterizing the equilibrium points and bounding the trajectories of nonlinear systems, and offers a concise and simple description of the main features of SOS programming, which can be used for general purpose in research and teaching.
Download or read book Statistical Extremes and Applications written by J. Tiago de Oliveira and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first references to statistical extremes may perhaps be found in the Genesis (The Bible, vol. I): the largest age of Methu'selah and the concrete applications faced by Noah-- the long rain, the large flood, the structural safety of the ark --. But as the pre-history of the area can be considered to last to the first quarter of our century, we can say that Statistical Extremes emer ged in the last half-century. It began with the paper by Dodd in 1923, followed quickly by the papers of Fre-chet in 1927 and Fisher and Tippett in 1928, after by the papers by de Finetti in 1932, by Gumbel in 1935 and by von Mises in 1936, to cite the more relevant; the first complete frame in what regards probabilistic problems is due to Gnedenko in 1943. And by that time Extremes begin to explode not only in what regards applications (floods, breaking strength of materials, gusts of wind, etc. ) but also in areas going from Proba bility to Stochastic Processes, from Multivariate Structures to Statistical Decision. The history, after the first essential steps, can't be written in few pages: the narrow and shallow stream gained momentum and is now a huge river, enlarging at every moment and flooding the margins. Statistical Extremes is, thus, a clear-cut field of Probability and Statistics and a new exploding area for research.
Download or read book Nonlinear and Optimal Control Systems written by Thomas L. Vincent and published by John Wiley & Sons. This book was released on 1997-06-23 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for one-semester introductory senior-or graduate-level course, the authors provide the student with an introduction of analysis techniques used in the design of nonlinear and optimal feedback control systems. There is special emphasis on the fundamental topics of stability, controllability, and optimality, and on the corresponding geometry associated with these topics. Each chapter contains several examples and a variety of exercises.
Download or read book An Intermediate Course in Probability written by Allan Gut and published by Springer Science & Business Media. This book was released on 2009-06-06 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the only book that gives a rigorous and comprehensive treatment with lots of examples, exercises, remarks on this particular level between the standard first undergraduate course and the first graduate course based on measure theory. There is no competitor to this book. The book can be used in classrooms as well as for self-study.
Download or read book Characterizations of Probability Distributions written by Janos Galambos and published by Springer. This book was released on 2006-11-15 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Operational Risk written by Harry H. Panjer and published by John Wiley & Sons. This book was released on 2006-10-13 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover how to optimize business strategies from both qualitative and quantitative points of view Operational Risk: Modeling Analytics is organized around the principle that the analysis of operational risk consists, in part, of the collection of data and the building of mathematical models to describe risk. This book is designed to provide risk analysts with a framework of the mathematical models and methods used in the measurement and modeling of operational risk in both the banking and insurance sectors. Beginning with a foundation for operational risk modeling and a focus on the modeling process, the book flows logically to discussion of probabilistic tools for operational risk modeling and statistical methods for calibrating models of operational risk. Exercises are included in chapters involving numerical computations for students' practice and reinforcement of concepts. Written by Harry Panjer, one of the foremost authorities in the world on risk modeling and its effects in business management, this is the first comprehensive book dedicated to the quantitative assessment of operational risk using the tools of probability, statistics, and actuarial science. In addition to providing great detail of the many probabilistic and statistical methods used in operational risk, this book features: * Ample exercises to further elucidate the concepts in the text * Definitive coverage of distribution functions and related concepts * Models for the size of losses * Models for frequency of loss * Aggregate loss modeling * Extreme value modeling * Dependency modeling using copulas * Statistical methods in model selection and calibration Assuming no previous expertise in either operational risk terminology or in mathematical statistics, the text is designed for beginning graduate-level courses on risk and operational management or enterprise risk management. This book is also useful as a reference for practitioners in both enterprise risk management and risk and operational management.
Download or read book Laws Of Small Numbers written by Michael Falk and published by Springer Science & Business Media. This book was released on 2004 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of the first edition of this seminar book in 1994, the theory and applications of extremes and rare events have enjoyed an enormous and still increasing interest. The intention of the book is to give a mathematically oriented development of the theory of rare events underlying various applications. This characteristic of the book was strengthened in the second edition by incorporating various new results on about 130 additional pages. Part II, which has been added in the second edition, discusses recent developments in multivariate extreme value theory. Particularly notable is a new spectral decomposition of multivariate distributions in univariate ones which makes multivariate questions more accessible in theory and practice. One of the most innovative and fruitful topics during the last decades was the introduction of generalized Pareto distributions in the univariate extreme value theory. Such a statistical modelling of extremes is now systematically developed in the multivariate framework.
Download or read book Statistics of Extremes written by Jan Beirlant and published by John Wiley & Sons. This book was released on 2004-10-15 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research in the statistical analysis of extreme values has flourished over the past decade: new probability models, inference and data analysis techniques have been introduced; and new application areas have been explored. Statistics of Extremes comprehensively covers a wide range of models and application areas, including risk and insurance: a major area of interest and relevance to extreme value theory. Case studies are introduced providing a good balance of theory and application of each model discussed, incorporating many illustrated examples and plots of data. The last part of the book covers some interesting advanced topics, including time series, regression, multivariate and Bayesian modelling of extremes, the use of which has huge potential.
Download or read book Stability and Performance of Control Systems with Actuator Saturation written by Yuanlong Li and published by Birkhäuser. This book was released on 2017-11-28 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph investigates the stability and performance of control systems subject to actuator saturation. It presents new results obtained by both improving the treatment of the saturation function and constructing new Lyapunov functions. In particular, two improved treatments of the saturation function are described that exploit the intricate structural properties of its traditional convex hull representation. The authors apply these treatments to the estimation of the domain of attraction and the finite-gain L2 performance by using the quadratic Lyapunov function and the composite quadratic Lyapunov function. Additionally, an algebraic computation method is given for the exact determination of the maximal contractively invariant ellipsoid, a level set of a quadratic Lyapunov function. The authors conclude with a look at some of the problems that can be solved by the methods developed and described throughout the book. Numerous step-by-step descriptions, examples, and simulations are provided to illustrate the effectiveness of their results. Stability and Performance of Control Systems with Actuator Saturation will be an invaluable reference for graduate students, researchers, and practitioners in control engineering and applied mathematics.
Download or read book The Biostatistics of Aging written by Gilberto Levy and published by John Wiley & Sons. This book was released on 2014-02-11 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: A practical and clarifying approach to aging and aging-related diseases Providing a thorough and extensive theoretical framework, The Biostatistics of Aging: From Gompertzian Mortality to an Index of Aging-Relatedness addresses the surprisingly subtlenotion—with consequential biomedical and public health relevance—of what it means for acondition to be related to aging. In this pursuit, the book presents a new quantitative methodto examine the relative contributions of genetic and environmental factors to mortality anddisease incidence in a population. With input from evolutionary biology, population genetics, demography, and epidemiology, this medically motivated book describes an index of aging-relatedness and also features: Original results on the asymptotic behavior of the minimum of time-to-event random variables, which extends those of the classical statistical theory of extreme values A comprehensive and satisfactory explanation based on biological principles of the Gompertz pattern of mortality in human populations The development of an evolution-based model of causation relevant to mortality and aging-related diseases of complex etiology An explanation of how and why the description of human mortality by the Gompertz distribution can be improved upon from first principles The amply illustrated analysis of real-world data, including a program for conducting the analysis written in the freely available R statistical software Technical appendices including mathematical material as well as an extensive and multidisciplinary bibliography on aging and aging-related diseases The Biostatistics of Aging: From Gompertzian Mortality to an Index of Aging-Relatedness is an excellent resource for practitioners and researchers with an interest in aging and aging-related diseases from the fields of medicine, biology, gerontology, biostatistics, epidemiology, demography, and public health.
Download or read book Laws of Small Numbers Extremes and Rare Events written by Michael Falk and published by Springer Science & Business Media. This book was released on 2010-10-07 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of the first edition of this seminar book in 1994, the theory and applications of extremes and rare events have enjoyed an enormous and still increasing interest. The intention of the book is to give a mathematically oriented development of the theory of rare events underlying various applications. This characteristic of the book was strengthened in the second edition by incorporating various new results. In this third edition, the dramatic change of focus of extreme value theory has been taken into account: from concentrating on maxima of observations it has shifted to large observations, defined as exceedances over high thresholds. One emphasis of the present third edition lies on multivariate generalized Pareto distributions, their representations, properties such as their peaks-over-threshold stability, simulation, testing and estimation. Reviews of the 2nd edition: "In brief, it is clear that this will surely be a valuable resource for anyone involved in, or seeking to master, the more mathematical features of this field." David Stirzaker, Bulletin of the London Mathematical Society "Laws of Small Numbers can be highly recommended to everyone who is looking for a smooth introduction to Poisson approximations in EVT and other fields of probability theory and statistics. In particular, it offers an interesting view on multivariate EVT and on EVT for non-iid observations, which is not presented in a similar way in any other textbook." Holger Drees, Metrika
Download or read book Control of Nonlinear and Hybrid Process Systems written by Panagiotis D. Christofides and published by Springer Science & Business Media. This book was released on 2005-10-04 with total page 736 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides insight and fundamental understanding into the feedback control of nonlinear and hybrid process systems. It presents state-of-the-art methods for the synthesis of nonlinear feedback controllers for nonlinear and hybrid systems with uncertainty, constraints and time-delays with numerous applications, especially to chemical processes. It covers both state feedback and output feedback (including state estimator design) controller designs. Control of Nonlinear and Hybrid Process Systems includes numerous comments and remarks providing insight and fundamental understanding into the feedback control of nonlinear and hybrid systems, as well as applications that demonstrate the implementation and effectiveness of the presented control methods. The book includes many detailed examples which can be easily modified by a control engineer to be tailored to a specific application. This book is useful for researchers in control systems theory, graduate students pursuing their degree in control systems and control engineers.
Download or read book Advances in Heavy Tailed Risk Modeling written by Gareth W. Peters and published by John Wiley & Sons. This book was released on 2015-05-05 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: A cutting-edge guide for the theories, applications, and statistical methodologies essential to heavy tailed risk modeling Focusing on the quantitative aspects of heavy tailed loss processes in operational risk and relevant insurance analytics, Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk presents comprehensive coverage of the latest research on the theories and applications in risk measurement and modeling techniques. Featuring a unique balance of mathematical and statistical perspectives, the handbook begins by introducing the motivation for heavy tailed risk processes in high consequence low frequency loss modeling. With a companion, Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk, the book provides a complete framework for all aspects of operational risk management and includes: Clear coverage on advanced topics such as splice loss models, extreme value theory, heavy tailed closed form loss distributional approach models, flexible heavy tailed risk models, risk measures, and higher order asymptotic approximations of risk measures for capital estimation An exploration of the characterization and estimation of risk and insurance modelling, which includes sub-exponential models, alpha-stable models, and tempered alpha stable models An extended discussion of the core concepts of risk measurement and capital estimation as well as the details on numerical approaches to evaluation of heavy tailed loss process model capital estimates Numerous detailed examples of real-world methods and practices of operational risk modeling used by both financial and non-financial institutions Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk is an excellent reference for risk management practitioners, quantitative analysts, financial engineers, and risk managers. The book is also a useful handbook for graduate-level courses on heavy tailed processes, advanced risk management, and actuarial science.
Download or read book Theory and Applications of Stochastic Processes written by Zeev Schuss and published by Springer Science & Business Media. This book was released on 2009-12-09 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic processes and diffusion theory are the mathematical underpinnings of many scientific disciplines, including statistical physics, physical chemistry, molecular biophysics, communications theory and many more. Many books, reviews and research articles have been published on this topic, from the purely mathematical to the most practical. This book offers an analytical approach to stochastic processes that are most common in the physical and life sciences, as well as in optimal control and in the theory of filltering of signals from noisy measurements. Its aim is to make probability theory in function space readily accessible to scientists trained in the traditional methods of applied mathematics, such as integral, ordinary, and partial differential equations and asymptotic methods, rather than in probability and measure theory.
Download or read book Ordered Random Variables Theory and Applications written by Muhammad Qaiser Shahbaz and published by Springer. This book was released on 2016-11-29 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ordered Random Variables have attracted several authors. The basic building block of Ordered Random Variables is Order Statistics which has several applications in extreme value theory and ordered estimation. The general model for ordered random variables, known as Generalized Order Statistics has been introduced relatively recently by Kamps (1995).
Download or read book Nonlinear Control Systems Design 1995 written by A.J. Krener and published by Elsevier. This book was released on 2016-01-22 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series of IFAC Symposia on Nonlinear Control Systems provides the ideal forum for leading researchers and practitioners who work in the field to discuss and evaluate the latest research and developments. This publication contains the papers presented at the 3rd IFAC Symposium in the series which was held in Tahoe City, California, USA.
