J.-P. Aubin; A. Cellina Differential Inclusions 9783642695148

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Автор: J.-P. Aubin; A. Cellina
Название: Differential Inclusions
ISBN: 9783642695148
Издательство: Springer
Классификация:

Основы высшей математики и математический анализ

ISBN-10: 3642695140
Обложка/Формат: Paperback
Страницы: 342
Вес: 0.51 кг.
Дата издания: 25.01.2012
Серия: Grundlehren der mathematischen Wissenschaften
Язык: English
Размер: 234 x 156 x 19
Основная тема: Mathematics
Подзаголовок: Set-Valued Maps and Viability Theory
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: 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, u)}ueu then solutions to the differential equations (*) are solutions to the differen- tial inclusion (**) x(t)EF(t, x(t)), x(O)=xo in which the controls do not appear explicitely. Systems Theory provides dynamical systems of the form d x(t)=A(x(t)) dt (B(x(t))] C(x(t)); x(O)=xo in which the velocity of the state of the system depends not only upon the x(t) of the system at time t, but also on variations of observations state B(x(t)) of the state. This is a particular case of an implicit differential equation f(t, x(t), x(t)) = 0 which can be regarded as a differential inclusion (**), where the right-hand side F is defined by F(t, x)= {vlf(t, x, v)=O}. During the 60s and 70s, a special class of differential inclusions was thoroughly investigated: those of the form X(t)E - A(x(t)), x (0) =xo where A is a maximal monotone map. This class of inclusions contains the class of gradient inclusions which generalize the usual gradient equations x(t) = -VV(x(t)), x(O)=xo when V is a differentiable potential. 2 Introduction There are many instances when potential functions are not differentiable.

Differential Inclusions, J.-P. Aubin; A. Cellina