Nonlinear Analysis Differential Equations And Control
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Nonlinear Analysis Differential Equations And Control
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Author : F.H. Clarke
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Analysis Differential Equations And Control written by F.H. Clarke and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Recent years have witnessed important developments in those areas of the mathematical sciences where the basic model under study is a dynamical system such as a differential equation or control process. Many of these recent advances were made possible by parallel developments in nonlinear and nonsmooth analysis. The latter subjects, in general terms, encompass differential analysis and optimization theory in the absence of traditional linearity, convexity or smoothness assumptions. In the last three decades it has become increasingly recognized that nonlinear and nonsmooth behavior is naturally present and prevalent in dynamical models, and is therefore significant theoretically. This point of view has guided us in the organizational aspects of this ASI. Our goals were twofold: We intended to achieve "cross fertilization" between mathematicians who were working in a diverse range of problem areas, but who all shared an interest in nonlinear and nonsmooth analysis. More importantly, it was our goal to expose a young international audience (mainly graduate students and recent Ph. D. 's) to these important subjects. In that regard, there were heavy pedagogical demands placed upon the twelve speakers of the ASI, in meeting the needs of such a gathering. The talks, while exposing current areas of research activity, were required to be as introductory and comprehensive as possible. It is our belief that these goals were achieved, and that these proceedings bear this out. Each of the twelve speakers presented a mini-course of four or five hours duration.
Constructive Experimental And Nonlinear Analysis
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Author : Michel A. Théra
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Constructive Experimental And Nonlinear Analysis written by Michel A. Théra and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
Presents 20 papers on different aspects of modern analysis including analytic and computational number theory, symbolic and numerical computation, theoretical and computational optimization, and recent development in non-smooth and functional analysis with applications to control theory. Applications in algorithmic number theory and tomography are also discussed. Many of the papers originated at a September 1999 workshop held at the University of Limoges. Among the topics are vector-valued perturbed minimization principles; rotundity related to Lipschitz separation; continued fractions, comparison algorithms, and fine structure constants; and codirectional compactness, metric regularity, and subdifferential calculus. No index. Annotation copyrighted by Book News, Inc., Portland, OR
Method Of Guiding Functions In Problems Of Nonlinear Analysis
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Author : Valeri Obukhovskii
language : en
Publisher: Springer
Release Date : 2013-05-13
Method Of Guiding Functions In Problems Of Nonlinear Analysis written by Valeri Obukhovskii and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-13 with Mathematics categories.
This book offers a self-contained introduction to the theory of guiding functions methods, which can be used to study the existence of periodic solutions and their bifurcations in ordinary differential equations, differential inclusions and in control theory. It starts with the basic concepts of nonlinear and multivalued analysis, describes the classical aspects of the method of guiding functions, and then presents recent findings only available in the research literature. It describes essential applications in control theory, the theory of bifurcations, and physics, making it a valuable resource not only for “pure” mathematicians, but also for students and researchers working in applied mathematics, the engineering sciences and physics.
Viability Invariance And Applications
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Author : Ovidiu Carja
language : en
Publisher: Elsevier
Release Date : 2007-07-18
Viability Invariance And Applications written by Ovidiu Carja and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-18 with Mathematics categories.
The book is an almost self-contained presentation of the most important concepts and results in viability and invariance. The viability of a set K with respect to a given function (or multi-function) F, defined on it, describes the property that, for each initial data in K, the differential equation (or inclusion) driven by that function or multi-function) to have at least one solution. The invariance of a set K with respect to a function (or multi-function) F, defined on a larger set D, is that property which says that each solution of the differential equation (or inclusion) driven by F and issuing in K remains in K, at least for a short time.The book includes the most important necessary and sufficient conditions for viability starting with Nagumo's Viability Theorem for ordinary differential equations with continuous right-hand sides and continuing with the corresponding extensions either to differential inclusions or to semilinear or even fully nonlinear evolution equations, systems and inclusions. In the latter (i.e. multi-valued) cases, the results (based on two completely new tangency concepts), all due to the authors, are original and extend significantly, in several directions, their well-known classical counterparts. - New concepts for multi-functions as the classical tangent vectors for functions - Provides the very general and necessary conditions for viability in the case of differential inclusions, semilinear and fully nonlinear evolution inclusions - Clarifying examples, illustrations and numerous problems, completely and carefully solved - Illustrates the applications from theory into practice - Very clear and elegant style
Nonlinear Analysis And Control Of Physical Processes And Fields
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Author : Mikhail Z. Zgurovsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Analysis And Control Of Physical Processes And Fields written by Mikhail Z. Zgurovsky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Modern achievements in the intensively developing field of applied mathematics are presented in this monograph. In particular, it proposes a new approach to extremal problem theory for nonlinear operators, differential-operator equations and inclusions, and for variational inequalities in Banach spaces. An axiomatic study of nonlinear maps (including multi-valued ones) is given, and the properties of resolving operators for systems, consisting of operator and differential-operator equations, are stated in nonlinear-map terms. The solvability conditions and the properties of extremal problem solutions are obtained, while their weak expansions and necessary conditions of optimality in variational inequality form are formulated. In addition. the monograph proposes regularization methods and approximation schemes. This book is adressed to scientists, graduates and undergraduates who are interested in nonlinear analysis, control theory, system analysis and differential equations.
Nonlinear Analysis Geometry And Applications
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Author : Diaraf Seck
language : en
Publisher: Springer Nature
Release Date : 2022-10-09
Nonlinear Analysis Geometry And Applications written by Diaraf Seck and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-09 with Mathematics categories.
This book gathers twenty-two papers presented at the second NLAGA-BIRS Symposium, which was held at Cap Skirring and at the Assane Seck University in Ziguinchor, Senegal, on January 25–30, 2022. The five-day symposium brought together African experts on nonlinear analysis and geometry and their applications, as well as their international partners, to present and discuss mathematical results in various areas. The main goal of the NLAGA project is to advance and consolidate the development of these mathematical fields in West and Central Africa with a focus on solving real-world problems such as coastal erosion, pollution, and urban network and population dynamics problems. The book addresses a range of topics related to partial differential equations, geometric analysis, geometric structures, dynamics, optimization, inverse problems, complex analysis, algebra, algebraic geometry, control theory, stochastic approximations, and modelling.
Applied Stochastic Control Of Jump Diffusions
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Author : Bernt Øksendal
language : en
Publisher: Springer
Release Date : 2019-04-17
Applied Stochastic Control Of Jump Diffusions written by Bernt Øksendal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-17 with Business & Economics categories.
The main purpose of the book is to give a rigorous introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and their applications. Both the dynamic programming method and the stochastic maximum principle method are discussed, as well as the relation between them. Corresponding verification theorems involving the Hamilton–Jacobi–Bellman equation and/or (quasi-)variational inequalities are formulated. The text emphasises applications, mostly to finance. All the main results are illustrated by examples and exercises appear at the end of each chapter with complete solutions. This will help the reader understand the theory and see how to apply it. The book assumes some basic knowledge of stochastic analysis, measure theory and partial differential equations. The 3rd edition is an expanded and updated version of the 2nd edition, containing recent developments within stochastic control and its applications. Specifically, there is a new chapter devoted to a comprehensive presentation of financial markets modelled by jump diffusions, and one on backward stochastic differential equations and convex risk measures. Moreover, the authors have expanded the optimal stopping and the stochastic control chapters to include optimal control of mean-field systems and stochastic differential games.
A Relaxation Based Approach To Optimal Control Of Hybrid And Switched Systems
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Author : Vadim Azhmyakov
language : en
Publisher: Butterworth-Heinemann
Release Date : 2019-02-14
A Relaxation Based Approach To Optimal Control Of Hybrid And Switched Systems written by Vadim Azhmyakov and has been published by Butterworth-Heinemann this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-14 with Technology & Engineering categories.
A Relaxation Based Approach to Optimal Control of Hybrid and Switched Systems proposes a unified approach to effective and numerically tractable relaxation schemes for optimal control problems of hybrid and switched systems. The book gives an overview of the existing (conventional and newly developed) relaxation techniques associated with the conventional systems described by ordinary differential equations. Next, it constructs a self-contained relaxation theory for optimal control processes governed by various types (sub-classes) of general hybrid and switched systems. It contains all mathematical tools necessary for an adequate understanding and using of the sophisticated relaxation techniques. In addition, readers will find many practically oriented optimal control problems related to the new class of dynamic systems. All in all, the book follows engineering and numerical concepts. However, it can also be considered as a mathematical compendium that contains the necessary formal results and important algorithms related to the modern relaxation theory. - Illustrates the use of the relaxation approaches in engineering optimization - Presents application of the relaxation methods in computational schemes for a numerical treatment of the sophisticated hybrid/switched optimal control problems - Offers a rigorous and self-contained mathematical tool for an adequate understanding and practical use of the relaxation techniques - Presents an extension of the relaxation methodology to the new class of applied dynamic systems, namely, to hybrid and switched control systems
Variational Analysis Of Regular Mappings
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Author : Alexander D. Ioffe
language : en
Publisher: Springer
Release Date : 2017-10-26
Variational Analysis Of Regular Mappings written by Alexander D. Ioffe and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-26 with Mathematics categories.
This monograph offers the first systematic account of (metric) regularity theory in variational analysis. It presents new developments alongside classical results and demonstrates the power of the theory through applications to various problems in analysis and optimization theory. The origins of metric regularity theory can be traced back to a series of fundamental ideas and results of nonlinear functional analysis and global analysis centered around problems of existence and stability of solutions of nonlinear equations. In variational analysis, regularity theory goes far beyond the classical setting and is also concerned with non-differentiable and multi-valued operators. The present volume explores all basic aspects of the theory, from the most general problems for mappings between metric spaces to those connected with fairly concrete and important classes of operators acting in Banach and finite dimensional spaces. Written by a leading expert in the field, the book covers new and powerful techniques, which have proven to be highly efficient even in classical settings, and outlines the theory’s predominantly quantitative character, leading to a variety of new and unexpected applications. Variational Analysis of Regular Mappings is aimed at graduate students and researchers in nonlinear and functional analysis, especially those working in areas close to optimization and optimal control, and will be suitable to anyone interested in applying new concepts and ideas to operations research, control engineering and numerical analysis.
Elliptic And Parabolic Problems Proceedings Of The 4th European Conference
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Author : Josef Bemelmans
language : en
Publisher: World Scientific
Release Date : 2002-08-06
Elliptic And Parabolic Problems Proceedings Of The 4th European Conference written by Josef Bemelmans and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-08-06 with Mathematics categories.
This book provides an overview of the state of the art in important subjects, including — besides elliptic and parabolic issues — geometry, free boundary problems, fluid mechanics, evolution problems in general, calculus of variations, homogenization, control, modeling and numerical analysis.