arXiv subjects

Brahim Sadik

Publications and source records attributed to Brahim Sadik.

5 recordsLinked to original sources

arXiv2025

Using infinitesimal symmetries for determining the first Maxwell time of geometric control problem on SH(2)

In this work, we utilize infinitesimal symmetries to compute Maxwell points which play a crucial role in studying sub-Riemannian control problems. By examining the infinitesimal symmetries of the geometric control problem on the SH(2) group, particularly through its Lie algebraic structure, we identify invariant quantities and constraints that streamline the Maxwell point computation.

math.OC↗

arXiv2022

A simple and constructive proof to a generalization of L\"uroth's theorem

A generalization of L{\"u}roth's theorem expresses that every transcendence degree 1 subfield of the rational function field is a simple extension. In this note we show that a classical proof of this theorem also holds to prove this generalization.

math.AC↗

arXiv2017

Un sous-syst\`eme d'un syst\`eme plat de dimension diff\'erentielle 2 est plat. A subsystem of a flat system of differential dimension 2 is flat

Un sous-syst\`eme de dimension diff\'erentielle au plus 2 d'une extension plate est plate. Si un tel syst\`eme plat est stationnaire, il admet des sorties plates ind\'ependantes du temps. A subsystem of a flat system of differential dimension at most 2 is flat. Furthermore, if such a flat system is stationary, we show that there exist flat utputs not depending on the time.

math.OC↗

arXiv2007

La borne de Jacobi pour une diffi{é}t{é} d{é}finie par un syst{è}me quasi r{é}gulier

We show that Jacobi's bound for the order of a system of ordinary differential equations stands in the case of a diffiety defined by a quasi-regular system. We extend the result when there are less equations than variables and characterize the case when the bound is reached.

math.DG↗

arXiv2007

Une méthode d'identification pour un système linéaire à retards

We provide a class of methods for the identification of a linear system with delay of the shape $x^{(n)}(t) = \sum_{i=0}^{n-1}a_{i}x^{(i)}(t) + bu(t-h)$. They allow the simultaneous identification of the parameters and delay, the observation of $x$ and its derivatives, knowing only generic input $u$ and output $x$. They are robust to the noise. Used in continuous time, they may follow the evolution of slowly varying parameters and noise. The method may be generalized to systems with two or more delays, e.g. $x''(t)+ax(t-h_{1})=bu(t-h_{2})$.

math.OC↗