Sur la stabilité des systèmes à retards variant dans le temps: théorie et application au contrôle de congestion d'un routeur
Yassine Ariba · HAL (Le Centre pour la Communication Scientifique Directe) · 2009
This thesis investigates the existing links between the control theory and the communication networks supporting the well-known communication protocol TCP. The key idea consists in using the tools from control theory for the network traffic stabilization. First, we have addressed the stability analysis of time-varying delay systems via two temporal approaches. On one hand, we consider the well-known Lyapunov-Krasovskii method in which new functionals are built according to original modelings of the system (delay fractionning , system derivative). On the other hand, the stability is also assessed with an input-output approach, borrowing then tools from the robust control framework. The time delay system is then rewritten as the interconnection of a linear application with a matrix consisting in a set of operators that defines the former system. Thus, having revisited the quadratic separation principle, additional auxiliary operators are proposed in order to provide an enhanced modeling of the delayed dynamic. In a second part, the developed methodology is used to cope with the congestion phenomenon in a router supporting TCP communications. This end-to-end protocol is sensitive to packet losses and adjusts thereof its sending rate with respect to the AIMD (Additive-Increase Multiplicative-Decrease) algorithm. Based on the Active Queue Management (AQM) principle, we design a controller embedded into the router that monitors the packet losses. A such mechanism allows to stabilize the network traffic and to control the congestion phenomenon in spite of the delays induced by the network. All theoretical results are tested through experiments under the network simulator NS-2.