# 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

### Differential Inclusions by J.-P. Aubin,A. Cellina

A great impetus to study differential inclusions came from the development of Control Theory, i.e. of dynamical systems x'(t) = f(t, x(t), u(t)), x(O)=xo "controlled" by parameters u(t) (the "controls"). Indeed, if we introduce the set-valued map F(t, x)= {f(t, x,

### Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces by Mikhail Kamenskii,Valeri Obukhovskii,Pietro Zecca

The theory of set-valued maps and of differential inclusion is developed in recent years both as a field of his own and as an approach to control theory. The book deals with the theory of semilinear differential inclusions in infinite dimensional spaces. In this setting, problems of interest to applications

### Impulsive Differential Inclusions by John R. Graef,Johnny Henderson,Abdelghani Ouahab

Differential equations with impulses arise as models of many evolving processes that are subject to abrupt changes, such as shocks, harvesting, and natural disasters. These phenomena involve short-term perturbations from continuous and smooth dynamics, whose duration is negligible in comparison with the duration of an entire evolution. In models involving

### Stochastic Differential Inclusions and Applications by Michał Kisielewicz

​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

### Differential Inclusions in a Banach Space by Alexander Tolstonogov

Preface to the English Edition The present monograph is a revised and enlarged alternative of the author's monograph [19] which was devoted to the development of a unified approach to studying differential inclusions, whose values of the right hand sides are compact, not necessarily convex subsets of a Banach space. This

### Approximation and Optimization of Discrete and Differential Inclusions by Elimhan N Mahmudov

Optimal control theory has numerous applications in both science and engineering. This book presents basic concepts and principles of mathematical programming in terms of set-valued analysis and develops a comprehensive optimality theory of problems described by ordinary and partial differential inclusions. In addition to including well-recognized results of variational analysis

### In Stability of Differential Inclusions by Philipp Braun,Lars Grüne,Christopher M. Kellett

Lyapunov methods have been and are still one of the main tools to analyze the stability properties of dynamical systems. In this monograph, Lyapunov results characterizing the stability and stability of the origin of differential inclusions are reviewed. To characterize instability and destabilizability, Lyapunov-like functions, called Chetaev and control Chetaev

### Theory of Control Systems Described by Differential Inclusions by Zhengzhi Han,Xiushan Cai,Jun Huang

This book provides a brief introduction to the theory of finite dimensional differential inclusions, and deals in depth with control of three kinds of differential inclusion systems. The authors introduce the algebraic decomposition of convex processes, the stabilization of polytopic systems, and observations of Luré systems. They also introduce the

### Differential Inclusions in a Banach Space by Alexander Tolstonogov

Preface to the English Edition The present monograph is a revised and enlarged alternative of the author's monograph [19] which was devoted to the development of a unified approach to studying differential inclusions, whose values of the right hand sides are compact, not necessarily convex subsets of a Banach space. This

### Viability Theory by Jean-Pierre Aubin,Alexandre M. Bayen,Patrick Saint-Pierre

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

This book focuses on the recent development of fractional differential equations, integro-differential equations, and inclusions and inequalities involving the Hadamard derivative and integral. Through a comprehensive study based in part on their recent research, the authors address the issues related to initial and boundary value problems involving Hadamard type differential

### Differential Equations with Impulse Effects by Nikolai A. Perestyuk,Viktor A. Plotnikov,Anatolii M. Samoilenko,Natalia V. Skripnik

This monograph is an introduction to the theory of ordinary differential equations with jump conditions at discrete moments of time. From the contents: Pulse differential equations and inclusions Linear systems with multivalued trajectories Method of averaging in systems with pulse action Averaging of differential inclusions Differential equations with discontinuous right-hand

### Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces by Mikhail I. Kamenskii,Valeri V. Obukhovskii,Pietro Zecca

The theory of set-valued maps and of differential inclusion is developed in recent years both as a field of his own and as an approach to control theory. The book deals with the theory of semilinear differential inclusions in infinite dimensional spaces. In this setting, problems of interest to applications

### Impulsive Differential Equations and Inclusions by Anonim

Download or read online Impulsive Differential Equations and Inclusions written by Anonim, published by Hindawi Publishing Corporation which was released on 2006. Get Impulsive Differential Equations and Inclusions Books now! Available in PDF, ePub and Kindle.