Displaying similar documents to “On the distribution of free path lengths for the periodic Lorentz gas II”

An optimal matching problem

Ivar Ekeland (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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Given two measured spaces ( X , μ ) and ( Y , ν ) , and a third space , given two functions  and , we study the problem of finding two maps s : X → Z and t : Y → Z such that the images s ( μ ) and t ( ν ) coincide, and the integral ∫ X u ( x , s ( x ) ) d μ - ∫ Y v ( y , t ( y ) ) d ν is maximal. We give condition on and for which there is a unique solution.

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...