# Introduction to the Theory of Differential Inclusions

Download or Read online Introduction to the Theory of Differential Inclusions full in PDF, ePub and kindle. This book written by Georgi V. Smirnov and published by American Mathematical Society which was released on 22 February 2022 with total pages 226. We cannot guarantee that Introduction to the Theory of Differential Inclusions book is available in the library, click Get Book button to download or read online books. Join over 650.000 happy Readers and READ as many books as you like.

 Author : Georgi V. Smirnov Publisher : American Mathematical Society Release Date : 22 February 2022 ISBN : 9781470468545 Pages : 226 pages Rating : /5 ( users)

## Download or Read Online Introduction to the Theory of Differential Inclusions in PDF, Epub and Kindle

A differential inclusion is a relation of the form \$dot x in F(x)\$, where \$F\$ is a set-valued map associating any point \$x in R^n\$ with a set \$F(x) subset R^n\$. As such, the notion of a differential inclusion generalizes the notion of an ordinary differential equation of the form \$dot x = f(x)\$. Therefore, all problems usually studied in the theory of ordinary differential equations (existence and continuation of solutions, dependence on initial conditions and parameters, etc.) can be studied for differential inclusions as well. Since a differential inclusion usually has many solutions starting at a given point, new types of problems arise, such as investigation of topological properties of the set of solutions, selection of solutions with given properties, and many others. Differential inclusions play an important role as a tool in the study of various dynamical processes described by equations with a discontinuous or multivalued right-hand side, occurring, in particular, in the study of dynamics of economical, social, and biological macrosystems. They also are very useful in proving existence theorems in control theory. This text provides an introductory treatment to the theory of differential inclusions. The reader is only required to know ordinary differential equations, theory of functions, and functional analysis on the elementary level. Chapter 1 contains a brief introduction to convex analysis. Chapter 2 considers set-valued maps. Chapter 3 is devoted to the Mordukhovich version of nonsmooth analysis. Chapter 4 contains the main existence theorems and gives an idea of the approximation techniques used throughout the text. Chapter 5 is devoted to the viability problem, i.e., the problem of selection of a solution to a differential inclusion that is contained in a given set. Chapter 6 considers the controllability problem. Chapter 7 discusses extremal problems for differential inclusions. Chapter 8 presents stability theory, and Chapter 9 deals with the stabilization problem.

### Introduction to the Theory of Differential Inclusions by Georgi V. Smirnov

A differential inclusion is a relation of the form \$dot x in F(x)\$, where \$F\$ is a set-valued map associating any point \$x in R^n\$ with a set \$F(x) subset R^n\$. As such, the notion of a differential inclusion generalizes the notion of an ordinary differential

### Introduction to the Theory of Differential Inclusions by Georgi V. Smirnov

Differential inclusions play an important role as a tool in the study of various dynamical processes described by equations with a discontinuous or multivalued right-hand side. This text acts as an introduction to the subject.

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Fuzzy differential functions are applicable to real-world problems in engineering, computer science, and social science. That relevance makes for rapid development of new ideas and theories. This volume is a timely introduction to the subject that describes the current state of the theory of fuzzy differential equations and inclusions and

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This brief examines mathematical models in nonsmooth mechanics and nonregular electrical circuits, including evolution variational inequalities, complementarity systems, differential inclusions, second-order dynamics, Lur'e systems and Moreau's sweeping process. The field of nonsmooth dynamics is of great interest to mathematicians, mechanicians, automatic controllers and engineers. The present volume acknowledges this transversality

### Multivalued Maps And Differential Inclusions Elements Of Theory And Applications by Obukhovskii Valeri,Gel'man Boris

Download or read online Multivalued Maps And Differential Inclusions Elements Of Theory And Applications written by Obukhovskii Valeri,Gel'man Boris, published by World Scientific which was released on 2020-04-04. Get Multivalued Maps And Differential Inclusions Elements Of Theory And Applications Books now! Available in PDF, ePub and Kindle.