Displaying similar documents to “An optimal matching problem”

Static Hedging of Barrier Options with a Smile: An Inverse Problem

Claude Bardos, Raphaël Douady, Andrei Fursikov (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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Let be a parabolic second order differential operator on the domain Π ¯ = 0 , T × . Given a function u ^ : R and x ^ > 0 such that the support of û is contained in ( - , - x ^ ] , we let y ^ : Π ¯ be the solution to the equation: L y ^ = 0 , y ^ | { 0 } × = u ^ . Given positive bounds 0 < x 0 < x 1 , we seek a function with support in x 0 , x 1 such that the corresponding solution satisfies: y ( t , 0 ) = y ^ ( t , 0 ) t 0 , T . We prove in this article that, under some regularity conditions on the coefficients of continuous solutions are unique and dense in the sense that y ^ | [ 0 , T ] × { 0 } can be -approximated,...

Controlled functional differential equations: approximate and exact asymptotic tracking with prescribed transient performance

Eugene P. Ryan, Chris J. Sangwin, Philip Townsend (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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A tracking problem is considered in the context of a class 𝒮 of multi-input, multi-output, nonlinear systems modelled by controlled functional differential equations. The class contains, as a prototype, all finite-dimensional, linear, -input, -output, minimum-phase systems with sign-definite “high-frequency gain". The first control objective is tracking of reference signals by the output of any system in 𝒮 : given λ 0 , construct a feedback strategy which ensures that, for every (assumed...