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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Differential Inclusions: Set-Valued Maps and Viability Theory

Differential Inclusions: Set-Valued Maps and Viability Theory

Aubin, J. -P
Cellina, A.

Paperback

Series: Grundlehren Der Mathematischen Wissenschaften, Book 264

General Mathematics

ISBN10: 3642695140
ISBN13: 9783642695148
Publisher: Springer Nature
Published: Jan 25 2012
Pages: 342
Weight: 1.12
Height: 0.75 Width: 6.14 Depth: 9.21
Language: English
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 60's and 70's, 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.

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