135 research outputs found
Regularity of Solutions of Retarded Equations and Application to Sensitivity of Linear Quadratic Controllers to Small Delays
AbstractWe analyze the behaviour of the solution of a linear differential equation of retarded type when the delays vary, for Lp initial conditions, given some p∈[1,∞]. First, we state continuity and differentiability results for the solution viewed as function of the delays. Those regularity results are applied to analyze the small delay sensitivity for quadratic performance index associated to stabilization with a finite dimensional a priori feedback
Multi-scale modeling of follicular ovulation as a reachability problem
During each ovarian cycle, only a definite number of follicles ovulate, while
the others undergo a degeneration process called atresia. We have designed a
multi-scale mathematical model where ovulation and atresia result from a
hormonal controlled selection process. A 2D-conservation law describes the age
and maturity structuration of the follicular cell population. In this paper, we
focus on the operating mode of the control, through the study of the
characteristics of the conservation law. We describe in particular the set of
microscopic initial conditions leading to the macroscopic phenomenon of either
ovulation or atresia, in the framework of backwards reachable sets theory
New Cardiovascular Indices Based on a Nonlinear Spectral Analysis of Arterial Blood Pressure Waveforms
A new method for analyzing arterial blood pressure is presented in this
report. The technique is based on the scattering transform and consists in
solving the spectral problem associated to a one-dimensional Schr\"odinger
operator with a potential depending linearly upon the pressure. This potential
is then expressed with the discrete spectrum which includes negative
eigenvalues and corresponds to the interacting components of an N-soliton. The
approach is similar to a nonlinear Fourier transform where the solitons play
the role of sine and cosine components. The method provides new cardiovascular
indices that seem to contain relevant physiological information. We first show
how to use this approach to decompose the arterial blood pressure pulse into
elementary waves and to reconstruct it or to separate its systolic and
diastolic phases. Then we analyse the parameters computed from this technique
in two physiological conditions, the head-up 60 degrees tilt test and the
isometric handgrip test, widely used for studying short term cardiovascular
control. Promising results are obtained
Experimental Evaluation of the Inverse Scattering Method for Electrical Cable Fault Diagnosis
International audienceRecently published theoretic and experimental results have shown the ability of inverse scattering-based methods to detect and to locate soft faults in electric cables, in particular, faults implying smooth spatial variations of cable characteristic parameters. The purpose of the present paper is to further experimentally evaluate the inverse scattering method for retrieving spatially distributed characteristic impedance from reflectometry measurements. With high quality coaxial cables connected in parallel, composite cables of piecewise constant characteristic impedance profiles are built in order to evaluate the accuracy of the inverse scattering method and its robustness in the presence of impedance discontinuities
Experimental validation of the inverse scattering method for distributed characteristic impedance estimation
International audience— Recently published theoretic results and numerical simulations have shown the ability of inverse scattering-based methods to diagnose soft faults in electric cables, in particular, faults implying smooth spatial variations of cable characteristic parameters. The purpose of the present paper is to report laboratory experiments confirming the ability of the inverse scattering method for retrieving spatially distributed characteristic impedance from reflectometry measurements. Various smooth or stepped spatial variations of characteristic impedance profiles are tested. The tested electric cables are CAN unshielded twisted pairs used in trucks and coaxial cables
On the inverse scattering of star-shape LC-networks
The study of the scattering data for a star-shape network of LC-transmission
lines is transformed into the scattering analysis of a Schr\"odinger operator
on the same graph. The boundary conditions coming from the Kirchhoff rules
ensure the existence of a unique self-adjoint extension of the mentioned
Schr\"odinger operator. While the graph consists of a number of infinite
branches and a number finite ones, all joining at a central node, we provide a
construction of the scattering solutions. Under non-degenerate circumstances
(different wave travelling times for finite branches), we show that the study
of the reflection coefficient in the high-frequency regime must provide us with
the number of the infinite branches as well as the the wave travelling times
for finite ones.Comment: 6 page
Input Impedance of the Arterial System Using Parametric Models
In this work, we propose to use parametric models for the estimation of arterial tree input impedance. The results of this new method are compared with those of the standard method based on the Fast Fourier Transform (FFT). The comparison is first made with pressure and flow measurements on a calf, then with human blood pressure measurements completed by blood flow data simulated from a soliton+windkessel model. The input impedance is calculated both at aorta and finger. As illustrated by the numerical results, the advantage of the proposed parametric method is its smooth impedance estimations, whereas the standard FFT method yields more disturbed results
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