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Viability Invariance And Applications

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Viability Invariance and Applications

Viability  Invariance and Applications Book
Author : Ovidiu Carja,Mihai Necula,Ioan I. Vrabie
Publisher : Elsevier
Release : 2007-07-18
ISBN : 9780080521664
Language : En, Es, Fr & De

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Book Description :

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

Viability Invariance and Applications

Viability  Invariance and Applications Book
Author : Ovidiu Carja,Mihai Necula,Ioan I. Vrabie
Publisher : Elsevier Science
Release : 2007-08-01
ISBN : 9780444527615
Language : En, Es, Fr & De

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Book Description :

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

Viability Invariance and Applications

Viability  Invariance and Applications Book
Author : Ovidiu Carja,Mihai Necula,Ioan I. Vrabie
Publisher : Elsevier Science
Release : 2007-08-01
ISBN : 9780444527615
Language : En, Es, Fr & De

GET BOOK

Book Description :

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

Viability Theory

Viability Theory Book
Author : Jean-Pierre Aubin,Alexandre M. Bayen,Patrick Saint-Pierre
Publisher : Springer Science & Business Media
Release : 2011-07-13
ISBN : 9783642166846
Language : En, Es, Fr & De

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Book Description :

Viability theory designs and develops mathematical and algorithmic methods for investigating the adaptation to viability constraints of evolutions governed by complex systems under uncertainty that are found in many domains involving living beings, from biological evolution to economics, from environmental sciences to financial markets, from control theory and robotics to cognitive sciences. It involves interdisciplinary investigations spanning fields that have traditionally developed in isolation. The purpose of this book is to present an initiation to applications of viability theory, explaining and motivating the main concepts and illustrating them with numerous numerical examples taken from various fields.

System Modeling and Optimization

System Modeling and Optimization Book
Author : Christian Pötzsche,Clemens Heuberger,Barbara Kaltenbacher,Franz Rendl
Publisher : Springer
Release : 2014-11-27
ISBN : 3662455048
Language : En, Es, Fr & De

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Book Description :

This book is a collection of thoroughly refereed papers presented at the 26th IFIP TC 7 Conference on System Modeling and Optimization, held in Klagenfurt, Austria, in September 2013. The 34 revised papers were carefully selected from numerous submissions. They cover the latest progress in a wide range of topics such as optimal control of ordinary and partial differential equations, modeling and simulation, inverse problems, nonlinear, discrete, and stochastic optimization as well as industrial applications.

Delay Differential Evolutions Subjected to Nonlocal Initial Conditions

Delay Differential Evolutions Subjected to Nonlocal Initial Conditions Book
Author : Monica-Dana Burlică,Mihai Necula,Daniela Roșu,Ioan I. Vrabie
Publisher : CRC Press
Release : 2018-09-03
ISBN : 1315351684
Language : En, Es, Fr & De

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Book Description :

Filling a gap in the literature, Delay Differential Evolutions Subjected to Nonlocal Initial Conditions reveals important results on ordinary differential equations (ODEs) and partial differential equations (PDEs). It presents very recent results relating to the existence, boundedness, regularity, and asymptotic behavior of global solutions for differential equations and inclusions, with or without delay, subjected to nonlocal implicit initial conditions. After preliminaries on nonlinear evolution equations governed by dissipative operators, the book gives a thorough study of the existence, uniqueness, and asymptotic behavior of global bounded solutions for differential equations with delay and local initial conditions. It then focuses on two important nonlocal cases: autonomous and quasi-autonomous. The authors next discuss sufficient conditions for the existence of almost periodic solutions, describe evolution systems with delay and nonlocal initial conditions, examine delay evolution inclusions, and extend some results to the multivalued case of reaction-diffusion systems. The book concludes with results on viability for nonlocal evolution inclusions.

Topological Structure of the Solution Set for Evolution Inclusions

Topological Structure of the Solution Set for Evolution Inclusions Book
Author : Yong Zhou,Rong-Nian Wang,Li Peng
Publisher : Springer
Release : 2017-10-31
ISBN : 9811066566
Language : En, Es, Fr & De

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Book Description :

This book systematically presents the topological structure of solution sets and attractability for nonlinear evolution inclusions, together with its relevant applications in control problems and partial differential equations. It provides readers the background material needed to delve deeper into the subject and explore the rich research literature. In addition, the book addresses many of the basic techniques and results recently developed in connection with this theory, including the structure of solution sets for evolution inclusions with m-dissipative operators; quasi-autonomous and non-autonomous evolution inclusions and control systems; evolution inclusions with the Hille-Yosida operator; functional evolution inclusions; impulsive evolution inclusions; and stochastic evolution inclusions. Several applications of evolution inclusions and control systems are also discussed in detail. Based on extensive research work conducted by the authors and other experts over the past four years, the information presented is cutting-edge and comprehensive. As such, the book fills an important gap in the body of literature on the structure of evolution inclusions and its applications.

Differential Equations

Differential Equations Book
Author : Ioan I. Vrabie
Publisher : World Scientific
Release : 2004
ISBN : 9789812388384
Language : En, Es, Fr & De

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Book Description :

This book presents the main concepts and results of differential equations, and offers the reader another point of view concerning a possible way to approach the problems of existence, uniqueness, approximation, and continuation of the solutions to a Cauchy problem. In addition, it contains simple introductions to some topics which are not usually included in classical textbooks: the exponential formula, conservation laws, generalized solutions, Caratheodory solutions, differential inclusions, variational inequalities, viability, invariance, gradient systems.

Co Semigroups and Applications

Co Semigroups and Applications Book
Author : Ioan I. Vrabie
Publisher : Elsevier
Release : 2003-03-21
ISBN : 9780080530048
Language : En, Es, Fr & De

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Book Description :

The book contains a unitary and systematic presentation of both classical and very recent parts of a fundamental branch of functional analysis: linear semigroup theory with main emphasis on examples and applications. There are several specialized, but quite interesting, topics which didn't find their place into a monograph till now, mainly because they are very new. So, the book, although containing the main parts of the classical theory of Co-semigroups, as the Hille-Yosida theory, includes also several very new results, as for instance those referring to various classes of semigroups such as equicontinuous, compact, differentiable, or analytic, as well as to some nonstandard types of partial differential equations, i.e. elliptic and parabolic systems with dynamic boundary conditions, and linear or semilinear differential equations with distributed (time, spatial) measures. Moreover, some finite-dimensional-like methods for certain semilinear pseudo-parabolic, or hyperbolic equations are also disscussed. Among the most interesting applications covered are not only the standard ones concerning the Laplace equation subject to either Dirichlet, or Neumann boundary conditions, or the Wave, or Klein-Gordon equations, but also those referring to the Maxwell equations, the equations of Linear Thermoelasticity, the equations of Linear Viscoelasticity, to list only a few. Moreover, each chapter contains a set of various problems, all of them completely solved and explained in a special section at the end of the book. The book is primarily addressed to graduate students and researchers in the field, but it would be of interest for both physicists and engineers. It should be emphasised that it is almost self-contained, requiring only a basic course in Functional Analysis and Partial Differential Equations.

Differential Equations

Differential Equations Book
Author : Ioan I Vrabie
Publisher : World Scientific Publishing Company
Release : 2016-05-30
ISBN : 981474980X
Language : En, Es, Fr & De

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Book Description :

This book presents, in a unitary frame and from a new perspective, the main concepts and results of one of the most fascinating branches of modern mathematics, namely differential equations, and offers the reader another point of view concerning a possible way to approach the problems of existence, uniqueness, approximation, and continuation of the solutions to a Cauchy problem. In addition, it contains simple introductions to some topics which are not usually included in classical textbooks: the exponential formula, conservation laws, generalized solutions, Caratheodory solutions, differential inclusions, variational inequalities, viability, invariance, and gradient systems. In this new edition, some typos have been corrected and two new topics have been added: Delay differential equations and differential equations subjected to nonlocal initial conditions. The bibliography has also been updated and expanded.

Mathematical Analysis and Applications

Mathematical Analysis and Applications Book
Author : V. Rădulescu,Vicentiu D. Radulescu,Constantin P. Niculescu
Publisher : American Institute of Physics
Release : 2006-05-25
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

This book comprises the proceedings of the International Conference on Mathematical Analysis and Applications, held in Craiova, Romania, 23-24 September 2005. The peer-reviewed papers presented here cover a range of topics at the interface between mathematical physics, numerical analysis, optimal control, and calculus of variations. The coverage includes nonlinear analysis and partial differential equations as well as classical mathematical analysis and dynamical systems.

Stochastic Differential Inclusions and Applications

Stochastic Differential Inclusions and Applications Book
Author : Michał Kisielewicz
Publisher : Springer Science & Business Media
Release : 2013-06-12
ISBN : 146146756X
Language : En, Es, Fr & De

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Book Description :

​This book aims to further develop the theory of stochastic functional inclusions and their applications for describing the solutions of the initial and boundary value problems for partial differential inclusions. The self-contained volume is designed to introduce the reader in a systematic fashion, to new methods of the stochastic optimal control theory from the very beginning. The exposition contains detailed proofs and uses new and original methods to characterize the properties of stochastic functional inclusions that, up to the present time, have only been published recently by the author. The work is divided into seven chapters, with the first two acting as an introduction, containing selected material dealing with point- and set-valued stochastic processes, and the final two devoted to applications and optimal control problems. The book presents recent and pressing issues in stochastic processes, control, differential games, optimization and their application in finance, manufacturing, queueing networks, and climate control. Written by an award-winning author in the field of stochastic differential inclusions and their application to control theory, This book is intended for students and researchers in mathematics and applications; particularly those studying optimal control theory. It is also highly relevant for students of economics and engineering. The book can also be used as a reference on stochastic differential inclusions. Knowledge of select topics in analysis and probability theory are required.

Nonlinear Partial Differential Equations with Applications

Nonlinear Partial Differential Equations with Applications Book
Author : Tomás Roubicek
Publisher : Springer Science & Business Media
Release : 2005-09-16
ISBN : 9783764372934
Language : En, Es, Fr & De

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Book Description :

This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition quickly leads general theory to analysis of concrete equations, which have specific applications in such areas as electrically (semi-) conductive media, modeling of biological systems, and mechanical engineering. Methods of Galerkin or of Rothe are exposed in a large generality.

Analele tiin ifice Ale Universit ii Al I Cuza Din Ia i

Analele   tiin  ifice Ale Universit    ii  Al  I  Cuza  Din Ia  i Book
Author : Anonim
Publisher : Unknown
Release : 2008
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Analele tiin ifice Ale Universit ii Al I Cuza Din Ia i book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Differential Equations

Differential Equations Book
Author : Ioan I Vrabie
Publisher : World Scientific Publishing Company
Release : 2011-05-26
ISBN : 9813108088
Language : En, Es, Fr & De

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Book Description :

This book presents, in a unitary frame and from a new perspective, the main concepts and results of one of the most fascinating branches of modern mathematics, namely differential equations, and offers the reader another point of view concerning a possible way to approach the problems of existence, uniqueness, approximation, and continuation of the solutions to a Cauchy problem. In addition, it contains simple introductions to some topics which are not usually included in classical textbooks: the exponential formula, conservation laws, generalized solutions, Caratheodory solutions, differential inclusions, variational inequalities, viability, invariance, gradient systems. In this new edition we have corrected several small errors and added the following new topics: Volterra Integral Equations and Elements of Calculus of Variations. Some problems and exercises, referring to these two new topics are also included. The bibliography has been updated and expanded.

Differential Games and Applications

Differential Games and Applications Book
Author : Tamer S. Başar,Tamer Başar,Pierre Bernhard
Publisher : Unknown
Release : 1989
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

This volume contains fifteen articles on the topic of differential and dynamic games, focusing on both theory and applications. It covers a variety of areas and presents recent developments on topics of current interest. It should be useful to researchers in differential and dynamic games, systems and control, operations research and mathematical economics.

Hierarchical Nonlinear Switching Control Design with Applications to Propulsion Systems

Hierarchical Nonlinear Switching Control Design with Applications to Propulsion Systems Book
Author : Alexander Leonessa,Wassim H. Haddad,Wassim M. Haddad,VijaySekhar Chellaboina,V. Chellaboina
Publisher : Springer Science & Business Media
Release : 2000-07-17
ISBN : 9781852333355
Language : En, Es, Fr & De

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Book Description :

This book presents a general nonlinear control design methodology for nonlinear uncertain dynamical systems. Specifically, a hierarchical nonlinear switching control framework is developed that provides a rigorous alternative to gain scheduling control for general nonlinear uncertain systems. The proposed switching control design framework accounts for actuator saturation constraints as well as system modeling uncertainty. The efficacy of the control design approach is extensively demonstrated on aeroengine propulsion systems. In particular, dynamic models for rotating stall and surge in axial and centrifugal flow compression systems that lend themselves to the application of nonlinear control design are developed and the hierarchical switching control framework is then applied to control the aerodynamic instabilities of rotating stall and surge. For the researcher who is entering the field of hierarchical switching robust control this book provides a plethora of new research directions. Alternatively, for researchers already active in the field of hierarchical control and hybrid systems, this book can be used as a reference to a significant body of recent work. Furthermore, control practitioners involved with nonlinear control design can immensely benefit from the novel nonlinear stabilization techniques presented in the book.

Intelligent Systems and Automation

Intelligent Systems and Automation Book
Author : Hichem Arioui,Rochdi Merzouki,Hadj Ahmed Abbassi
Publisher : American Institute of Physics
Release : 2008-06-17
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Annaba, Algeria, 30 June - 2 July 2008

Dynamic Systems and Applications

Dynamic Systems and Applications Book
Author : Anonim
Publisher : Unknown
Release : 2003
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Dynamic Systems and Applications book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

SIAM Journal on Control and Optimization

SIAM Journal on Control and Optimization Book
Author : Society for Industrial and Applied Mathematics
Publisher : Unknown
Release : 2008
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download SIAM Journal on Control and Optimization book written by Society for Industrial and Applied Mathematics, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.