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