On Designing Lyapunov-Krasovskii Based AQM for Routers Supporting TCP Flows

For the last few years, we assist to a growing interest of designing AQM (Active Queue Management) using control theory. In this paper, we focus on the synthesis of an AQM based on the Lyapunov theory for time delay systems. With the help of a recently developed Lyapunov-Krasovskii functional and using a state space representation of a linearized fluid model of TCP, two robust AQMs stabilizing the TCP model are constructed. Notice that our results are constructive and the synthesis problem is reduced to a convex optimization scheme expressed in terms of linear matrix inequalities (LMIs). Finally, an example extracted from the literature and simulations via {\it NS simulator} support our study

Robust Stability and Design of State Feedback Controller for Straightforward Active Queue Management

The straightforward active queue management ($AQM$), which is based on the prediction of arrival rate is investigated by means of state-space approach. We formulate the feedback control design problem for linearized system of additive increase multiplicative decrease ($AIMD$) dynamic models as state-space model. Then the Lyapunov-Krasovskii method is provided to achieve the robust stability and sufficient stabilization condition and afterwards the term of linear inequality matrix ($LMI$) is used to show the results. We present the simulation results and show the superiority of our proposed method to other control mechanisms

Design of a robust Controller/Observer for TCP/AQM network: First application to intrusion detection systems for drone fleet

International audienceThis paper proposes a robust controller/observer for UAVs network anomaly estimation which is based on both Lyapunov Krasovkii functional and dynamic behavior of TCP (Transmission Control Protocol). Several research works on network anomaly estimation have been led using automatic control techniques and provide methods for designing both observer and command laws dedicated to time delay problem while estimating the anomaly or intrusion in the system. The observer design is based on a linearized fluid-flow model of the TCP behavior and must be associated to an AQM (Active Queue Management) to perform its diagnosis. The developed robust controller/observer in this paper has to be tuned by considering the time delay linear state-space representation of TCP model. As a first result, the designed controller/observer system has been successfully applied to some relevant practical problems such as topology network for aerial vehicles and the effectiveness is illustrated by using real traffic traces including Denial of Service attacks. Our first results show promising perspectives for Intrusion Detection System (IDS) in a fleet of UAVs

Robust control tools for traffic monitoring in TCP/AQM networks

Several studies have considered control theory tools for traffic control in communication networks, as for example the congestion control issue in IP (Internet Protocol) routers. In this paper, we propose to design a linear observer for time-delay systems to address the traffic monitoring issue in TCP/AQM (Transmission Control Protocol/Active Queue Management) networks. Due to several propagation delays and the queueing delay, the set TCP/AQM is modeled as a multiple delayed system of a particular form. Hence, appropriate robust control tools as quadratic separation are adopted to construct a delay dependent observer for TCP flows estimation. Note that, the developed mechanism enables also the anomaly detection issue for a class of DoS (Denial of Service) attacks. At last, simulations via the network simulator NS-2 and an emulation experiment validate the proposed methodology

Análisis de estabilidad de controladores AQM proporcional-integral suportando flujos TCP

"Este artículo se centra en la estabilidad asintótica de controladores AQM del tipo proporcional–integral suportando flujos TCP . Se proporcionan condiciones necesarias y suficientes para la estabilidad asintótica de la linealización del sistema en lazo cerrado. Como un resultado, se obtiene el conjunto completo de controladores proporcional–integral que estabiliza localmente el punto de equilibrio. También se aborda la robustez de los controladores a incertidumbres en los parámetros de red (número de sesiones TCP, tiempo de viaje completo y capacidad del enlace). Se muestra que diseñando el controlador con respecto a los valores más grandes esperados para el retardo y la capacidad del enlace, y el valor más pequeño esperado para las cargas de TCP nos proporciona el conjunto completo de controladores robustos."This paper focuses on the asymptotic stability of proportional-integral AQM controllers supporting TCP flows. Necessary and sufficient conditions for the asymptotic stability of the closed-loop linearization are provided. As a result, the complete set of proportional-integral controllers that locally stabilizes the equilibrium point is obtained. The robustness of the controllers to uncertainties in the network parameters (number of TCP flows, round-trip time and link capacity) is also addressed. It is shown that designing the controller with respect to the largest expected values of delay and link capacity, and the smallest expected value of TCP loads leads to the complete set of robust stabilizing controllers

Network flow optimization and distributed control algorithms

This thesis concerns the problem of designing distributed algorithms for achieving efficient and fair bandwidth allocations in a resource constrained network. This problem is fundamental to the design of transmission protocols for communication networks, since the fluid models of popular protocols such as TCP and Proportional Fair Controller can be viewed as distributed algorithms which solve the network flow optimization problems corresponding to some fairness criteria. Because of the convexity of the optimization problem as well as its decoupling structure, there exist classical dual algorithm and primal/dual algorithm which are both distributed. However, the main difficulty is the possible instability of the dynamics of these algorithms caused by transmission delays. We use customized Lyapunov-Krasovskii functionals to obtain the stability conditions for these algorithms in networks with heterogeneous time-varying delays. There are two main features of our results. The first is that these stability conditions can be enforced by a small amount of information exchange among relevant users and links. The second is that these stability conditions only depend on the upper bound of delays, not on the rate of delay variations. We further our discussion on scalable algorithms with minimum information to maintain stability. We present a design methodology for such algorithms and prove the global stability of our scalable controllers by the use of Zames-Falb multipliers. Next we extend this method to design the first scalable and globally stable algorithm for the joint multipath routing and flow optimization problem. We achieve this by adding additional delays to different paths for all users. Lastly we discuss the joint single path routing and flow optimization problem, which is a NP hard problem. We show bounded price of anarchy for combined flow and routing game for simple networks and show for many-user networks, simple Nash algorithm leads to approximate optimum of the problem

congestion control in tcp/ip routers based on sampled-data systems theory

Producción CientíficaA methodology for designing congestion controllers, based on active queue management (AQM), is presented here. The congestion control law is derived using sampled-data H∞ systems theory. More precisely, a sampled-data state feedback that guarantees the stability of the closed-loop system and satisfies a H∞ disturbance attenuation level is derived here, based on sufficient conditions expressed in terms of linear matrix inequalities. The effectiveness of the developed technique is validated on two examples

Multiple time-delays system modeling and control for router management

Abstract-This paper investigates the overload problem of a single congested router in TCP (Transmission Control Protocol) networks. To cope with the congestion phenomenon, we design a feedback control based on a multiple time-delays model of the set TCP/AQM (Active Queue Management). Indeed, using robust control tools, especially in the quadratic separation framework, the TCP/AQM model is rewritten as an interconnected system and a structured state feedback is constructed to stabilize the network variables. Finally, we illustrate the proposed methodology with a numerical example and simulations using NS-2 [1] simulator

Internet Congestion Control: Modeling and Stability Analysis

The proliferation and universal adoption of the Internet has made it become the key information transport platform of our time. Congestion occurs when resource demands exceed the capacity, which results in poor performance in the form of low network utilization and high packet loss rate. The goal of congestion control mechanisms is to use the network resources as efficiently as possible. The research work in this thesis is centered on finding ways to address these types of problems and provide guidelines for predicting and controlling network performance, through the use of suitable mathematical tools and control analysis. The first congestion collapse in the Internet was observed in 1980's. To solve the problem, Van Jacobson proposed the Transmission Control Protocol (TCP) congestion control algorithm based on the Additive Increase and Multiplicative Decrease (AIMD) mechanism in 1988. To be effective, a congestion control mechanism must be paired with a congestion detection scheme. To detect and distribute network congestion indicators fairly to all on-going flows, Active Queue Management (AQM), e.g., the Random Early Detection (RED) queue management scheme has been developed to be deployed in the intermediate nodes. The currently dominant AIMD congestion control, coupled with the RED queue in the core network, has been acknowledged as one of the key factors to the overwhelming success of the Internet. In this thesis, the AIMD/RED system, based on the fluid-flow model, is systematically studied. In particular, we concentrate on the system modeling, stability analysis and bounds estimates. We first focus on the stability and fairness analysis of the AIMD/RED system with a single bottleneck. Then, we derive the theoretical estimates for the upper and lower bounds of homogeneous and heterogeneous AIMD/RED systems with feedback delays and further discuss the system performance when it is not asymptotically stable. Last, we develop a general model for a class of multiple-bottleneck networks and discuss the stability properties of such a system. Theoretical and simulation results presented in this thesis provide insights for in-depth understanding of AIME/RED system and help predict and control the system performance for the Internet with higher data rate links multiplexed with heterogeneous flows