Résumé:

At this seminar K.E. Avrachenkov is going to present a brief overview  of his main research results obtained during the last years. The main contributions of the speaker are in the areas of iterative learning  control, analytic perturbation theory and internet traffic modelling.  The presentation is respectively divided in three parts.

1. The iterative learning control (ILC) methods are used to control systems working in the cyclic regime. The examples of such systems are robotic manipulators, hard-disc drivers and chemical processing plants. ILC schemes use the errors from the previous cycles to improve the system performance on the next cycle. One can show that ILC can be viewed as online iterative solution of operator equations.

2. The purpose of analytic perturbation theory is to study the properties of linear operators  depending analytically on a small parameter. This general theory has numerous applications,  since it is often of great interest to know the behaviour of some system in respect to the change of its parameters. Furthermore, analytic perturbation approach provides a method of  approximation of complex systems by simpler ones. At the seminar, several applications of  analytic perturbation theory to Markov chains, Markov Decision Processes and Mathematical  Programming will be presented.

3. Finally, the speaker will present the results on TCP/IP (Internet traffic control mechanism)  modelling which were obtained during the speaker's sejour in INRIA. In the Internet data is sent over network in packets and the number of packets that can be send without receiving  acknowledgement is controlled by means of the congestion window. The speaker will present several models for the description of the congestion  window evolution.