Differential Inclusions: Set-Valued Maps and Viability Theory - Couverture souple

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

9783642695148: Differential Inclusions: Set-Valued Maps and Viability Theory

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ISBN 10 : 3642695140 ISBN 13 : 9783642695148

Editeur : Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 2012

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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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�diteur: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Date d'�dition: 2012
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ISBN 10: 3642695140
ISBN 13: 9783642695148
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Differential Inclusions. Set-Valued Maps and Viability Theory.

Aubin, Jean-Pierre

Edit� par Berlin/Heidelberg, Springer., 1984

ISBN 10 : 3642695140 ISBN 13 : 9783642695148

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XIII, 342p. Broschur. Versand aus Deutschland / We dispatch from Germany via Air Mail. Einband besto�en, daher M�ngelexemplar gestempelt, sonst sehr guter Zustand. Imperfect copy due to slightly bumped cover, apart from this in very good condition. Stamped. Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 264. Sprache: Englisch. N� de r�f. du vendeur 7196BB

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Differential Inclusions

J.-P. Aubin|A. Cellina

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Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 0. Background Notes.- 1. Continuous Partitions of Unity.- 2. Absolutely Continuous Functions.- 3. Some Compactness Theorems.- 4. Weak Convergence and Asymptotic Center of Bounded Sequences.- 5. Closed Convex Hulls and the Mean-Value Theorem.- 6. Lower Semic. N� de r�f. du vendeur 5068306

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Differential Inclusions: Set-Valued Maps and Viability Theory (Grundlehren der mathematischen Wissenschaften, 264)

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

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Differential Inclusions : Set-Valued Maps and Viability Theory

A. Cellina

Edit� par Springer Berlin Heidelberg, 2012

ISBN 10 : 3642695140 ISBN 13 : 9783642695148

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Taschenbuch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. N� de r�f. du vendeur 9783642695148

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Differential Inclusions

A. Cellina

Edit� par Springer Berlin Heidelberg Jan 2012, 2012

ISBN 10 : 3642695140 ISBN 13 : 9783642695148

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Taschenbuch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 364 pp. Englisch. N� de r�f. du vendeur 9783642695148

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Differential Inclusions

A. Cellina

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ISBN 10 : 3642695140 ISBN 13 : 9783642695148

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Taschenbuch. Etat : Neu. Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 364 pp. Englisch. N� de r�f. du vendeur 9783642695148

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