Differential Inclusions : Set-Valued Maps and Viability Theory
Aubin, Jean-Pierre; Cellina, Arrigo
ISBN 10: 3642695140 ISBN 13: 9783642695148
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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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Title: Differential Inclusions : Set-Valued Maps ...
Publisher: Springer
Publication Date: 2012
Binding: Soft cover
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Condition: 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. Seller Inventory # 5068306
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Taschenbuch. Condition: Neu. Differential Inclusions | Set-Valued Maps and Viability Theory | J. -P. Aubin (u. a.) | Taschenbuch | xiii | Englisch | 2012 | Springer | EAN 9783642695148 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu. Seller Inventory # 106331156
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Paperback. Condition: new. Paperback. 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. 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 "differenA 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 Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9783642695148
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Differential Inclusions
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Taschenbuch. Condition: Neu. This item is printed on demand - Print on Demand Titel. 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. Seller Inventory # 9783642695148
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Differential Inclusions : Set-Valued Maps and Viability Theory
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Taschenbuch. Condition: 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. Seller Inventory # 9783642695148
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Differential Inclusions
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Taschenbuch. Condition: 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. Seller Inventory # 9783642695148
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Differential Inclusions: Set-Valued Maps and Viability Theory (Grundlehren der mathematischen Wissenschaften, 264)
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Differential Inclusions: Setvalued Maps and Viability Theory (Grundlehren Der Mathematischen Wissenschaften)
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