On the use of State Predictors in Networked Control Systems

International audienceWithout pretending to be exhaustive, the aim of this chapter is to give an overview on the use of the state predictor in the context of time-delay systems, and more particularly for the stabilisation of networked control systems. We show that the stabilisation of a system through a deterministic network can be considered as the stabilisation of a time-delayed system with a delay of known dynamics. The predictor approach is proposed, along with some historical background on its application to time-delayed systems, to solve this problem. Some simulation results are also presented

The ReLPM Exponential Integrator for FE Discretizations of Advection-Diffusion Equations

We implement an exponential integrator for large and sparse systems of ODEs, generated by FE (Finite Element) discretization with mass-lumping of advection-diffusion equations. The relevant exponential-like matrix function is approximated by polynomial interpolation, at a sequence of real Leja points related to the spectrum of the FE matrix (ReLPM, Real Leja Points Method). Application to 2D and 3D advection-dispersion models shows speed-ups of one order of magnitude with respect to a classical variable step-size Crank-Nicolson solver

Actes du deuxième colloque africain sur la recherche en informatique = Proceedings of the second African Conference on research in computer science

Numerical methods related on Krylov subspaces are widely used in large sparse numerical linear algebra. Vectors in these subspaces are manipulated through their representation onto orthonormal bases. Nowadays, on serial computers, the method of Arnoldi is considered as a reliable technique for constructing such bases. Unfortunately, this technique is rather inflexible to be efficiently implemented on parallel computers. In this report we examine several parallel and stable algorithms based on the idea of Reichel et al. which retrieve at their completion the same information as the sequential Arnoldi's method. We present timing results obtained from their implementations on the Intel Paragon distributed-memory multiprocessor machine. (Résumé d'auteur

Fortschritte der initialen Verätzungstherapie : zwei Augenspüllösungen im Vergleich

We have implemented a numerical code (ReLPM, Real Leja Points Method) for polynomial interpolation of the matrix exponential propagators exp (Delta tA) v and phi(Delta tA) v, phi(z) = (exp (z) - 1)/z. The ReLPM code is tested and compared with Krylov-based routines, on large scale sparse matrices arising from the spatial discretization of 2D and 3D advection-diffusion equations