An Observer-Based Controller for Congestion Control in Data Networks
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An Observer-Based Controller for Congestion Control in Data Networks Nabil El Fezazi1 Received: 11 March 2019 / Revised: 22 May 2019 / Accepted: 20 June 2019 © Brazilian Society for Automatics–SBA 2019
Abstract This paper investigates the design of an observer-based controller to overcome the congestion problem in the TCP/IP networks where the available link bandwidth is modeled as a time-variant disturbance. Then, a detailed description is discussed to establish a linearized mathematical model in order to ensure the robust stability of the saturated delayed system and satisfy the H∞ performance. Based on a Lyapunov–Krasovskii (L–K) functional, a generalized sector condition, and the Finsler’s Lemma, the proposed new design methodology leads to a quite simple LMI condition that is numerically tractable with any convex optimization algorithm. An effective iterative optimization algorithm is adopted to estimate the largest possible region of initial conditions as will be seen in the numerical examples where the results are compared to PI, RED, and REM controllers. Keywords Observer-based controller · Congestion · TCP/IP networks · Available link bandwidth · Saturated delayed system
1 Introduction Internet users rely on the good capabilities of TCP/IP networks for dealing with congestion that is the key factor in performance degradation. Active queue management (AQM) is an effective congestion control mechanism at the intermediate nodes, which can keep the best-effort service with low delay. Many AQM schemes have been proposed to increase network utilization by regulating queues at the bottleneck links in TCP/IP networks. The simplest AQM is Drop Tail, which drops packets arriving at a router when its buffer is already full. As emphasized in Hollot et al. (2002), this leads to flow synchronization and performance degradation, due to excessive timeouts and restarts. Then, random early detection (RED) was proposed (Floyd and Jacobson 1993; Hollot et al. 2001a) to introduce probabilistic early packet dropping in order to avoid full queues: sources then adapt the flows. However, RED is hard to tune adequately and RED might still cause oscillations and instability due to the parameter variations in the network. In Misra et al. (2000), a fluid model of TCP dynamical behavior was derived by using the theory of stochastic differential equations, allowing to use tradi-
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Nabil El Fezazi [email protected] LESSI, Department of Physics, Faculty of Sciences Dhar El Mehraz, University Sidi Mohammed Ben Abdellah, BP 1796, Fes-Atlas, Morocco
tional controllers, such as proportional integral (PI) (Hollot et al. 2001b), proportional derivative (PD) (Sun et al. 2003), proportional integral derivative (PID) (Yanfie et al. 2003). On other hand, the key idea of random exponential marking (REM) is to decouple congestion measure (price) from performance measure (loss and queue), so that a performance measure can be regulated around its target despite variations with the number of sources (Athuraliya et al. 2001). We emphasize, howev
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