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sigurdurhafsteinSiguršur Freyr Hafstein, dr. rer. nat.

Associate Professor
School of Science and Engineering
Kringlunni 1
IS-103 Reykjavik
Iceland

Telephone: +354 599 6325
Email: sigurdurh@ru.is

 

Biography

In the last 5 years I have been working on two quite different subjects.

First, I designed and programmed a traffic-simulator that is used to estimate and forecast the traffic-load on the autobahn-network in North Rhine - Westphalia (NRW), which is the most populous German federal-state.  The simulator gets real-time traffic-data every minute from more than 4,000 loop-detectors that are installed on the streets.  This data is used to estimate the traffic- load on the autobahn network (> 12,000 km street-lanes) and to forecast future traffic-loads.  The former minister of transport in NRW, Dr. Axel Horstmann, opened the webpage www.autobahn.nrw.de to the public in September 2002.  There the simulated traffic-load and traffic-forecasts for 30 and 60 minutes, generated by the simulator, are presented.  In 2003 I got the Heinz-Billing Prize of the Max-Planck Institute for my work on this project. 

Second, I have been studying the stability of solutions to ordinary differential equations.  Especially, I designed an algorithm that uses linear programming to generate non-local Lyapunov-functions for uniformly asymptotically stable (UAS) equilibria.  Lyapunov-functions are the generalization of the physical concept "energy" to general ODEs.  This research is summed up in the monograph:  

Sigurdur Freyr Hafstein. 
An algorithm for constructing Lyapunov functions.
Electronic Journal of Differential Equations, Monograph 08 (2007).

Accessed online at  http://ejde.math.txstate.edu/

In this work the problem of generating Lyapunov-functions for ODEs with UAS equilibrium by a computer is, to my best knowledge, in essence satisfactorily solved  (it always works if the function f in the ODE dx/dt = f(t,x) is C^2). 

At the moment I am programming a more user friendly program in C++ to make the algorithm to construct Lyapunov-functions for nonlinear systems available to scientists and system engineers, that are not necessarily eager to read well over hundred pages of quite technical mathematics before programming it them self.  When it is done, it will be downloadable at this website free of charge.