C. V. Hollot

On designing improved controllers for AQM routers supporting TCP flows

In this paper we study a previously developed linearized model of TCP and active queue management (AQM). We use classical control system techniques to develop controllers well suited for the application. The controllers are shown to have better theoretical properties than the well known RED controller. We present guidelines for designing stable controllers subject to network parameters like load level propagation delay etc. We also present simple implementation techniques which require a minimal change to RED implementations. The performance of the controllers are verified and compared with RED using ns simulations. The second of our designs, the proportional integral (PI) controller is shown to outperform RED significantly.

A control theoretic analysis of RED

We use a previously developed nonlinear dynamic model of TCP to analyze and design active queue management (AQM) control systems using random early detection (RED). First, we linearize the interconnection of TCP and a bottlenecked queue and discuss its feedback properties in terms of network parameters such as link capacity, load and round-trip time. Using this model, we next design an AQM control system using the RED scheme by relating its free parameters such as the low-pass filter break point and loss probability profile to the network parameters. We present guidelines for designing linearly stable systems subject to network parameters like propagation delay and load level. Robustness to variations in system loads is a prime objective. We present no simulations to support our analysis.

Analysis and design of controllers for AQM routers supporting TCP flows

In active queue management (AQM), core routers signal transmission control protocol (TCP) sources with the objective of managing queue utilization and delay. It is essentially a feedback control problem. Based on a recently developed dynamic model of TCP congestion-avoidance mode, this paper does three things: 1) it relates key network parameters such as the number of TCP sessions, link capacity and round-trip time to the underlying feedback control problem; 2) it analyzes the present de facto AQM standard: random early detection (RED) and determines that REDs queue-averaging is not beneficial; and 3) it recommends alternative AQM schemes which amount to classical proportional and proportional-integral control. We illustrate our results using ns simulations and demonstrate the practical impact of proportional-integral control on managing queue utilization and delay.

A Riccati equation approach to the stabilization of uncertain linear systems

This paper presents a method for designing a feedback control law to stabilize a class of uncertain linear systems. The systems under consideration contain uncertain parameters whose values are known only to within a given compact bounding set. Furthermore, these uncertain parameters may be time-varying. The method used to establish asymptotic stability of the closed loop system (obtained when the feedback control is applied) involves the use of a quadratic Lyapunov function. The main contribution of this paper involves the development of a computationally feasible algorithm for the construction of a suitable quadratic Lyapunov function. Once the Lyapunov function has been obtained, it is used to construct the stabilizing feedback control law. The fundamental idea behind the algorithm presented involves constructing an upper bound for the Lyapunov derivative corresponding to the closed loop system. This upper bound is a quadratic form. By using this upper bounding procedure, a suitable Lyapunov function can be found by solving a certain matrix Riccati equation. Another major contribution of this paper is the identification of classes of systems for which the success of the algorithm is both necessary and sufficient for the existence of a suitable quadratic Lyapunov function.

Root locations of an entire polytope of polynomials: It suffices to check the edges

The presence of uncertain parameters in a state space or frequency domain description of a linear, time-invariant system manifests itself as variability in the coefficients of the characteristic polynomial. If the family of all such polynomials is polytopic in coefficient space, we show that the root locations of the entire family can be completely determined by examining only the roots of the polynomials contained in the exposed edges of the polytope. These procedures are computationally tractable, and this criterion improves upon the presently available stability tests for uncertain systems, being less conservative and explicitly determining all root locations. Equally important is the fact that the results are also applicable to discrete-time systems.

Multi-path TCP: a joint congestion control and routing scheme to exploit path diversity in the internet

We consider the problem of congestion-aware multi-path routing in the Internet. Currently, Internet routing protocols select only a single path between a source and a destination. However, due to many policy routing decisions, single-path routing may limit the achievable throughput. In this paper, we envision a scenario where multi-path routing is enabled in the Internet to take advantage of path diversity. Using minimal congestion feedback signals from the routers, we present a class of algorithms that can be implemented at the sources to stably and optimally split the flow between each source-destination pair. We then show that the connection-level throughput region of such multi-path routing/congestion control algorithms can be larger than that of a single-path congestion control scheme

Fundamental properties of reset control systems

Reset controllers are linear controllers that reset some of their states to zero when their input is zero. We are interested in their feedback connection with linear plants, and in this paper we establish fundamental closed-loop properties including stability and asymptotic tracking. This paper considers more general reset structures than previously considered, allowing for higher-order controllers and partial-state resetting. It gives a testable necessary and sufficient condition for quadratic stability and links it to both uniform bounded-input bounded-state stability and steady-state performance. Unlike previous related research, which includes the study of impulsive differential equations, our stability results require no assumptions on the evolution of reset times.

Extreme point results for robust stabilization of interval plants with first-order compensators

It has been shown previously that a first-order compensator robustly stabilizes an internal plant family if and only if it stabilizes all of the extreme plants. These extreme plants are obtained by considering all possible combinations for the extreme values of the numerator and denominator coefficients. In this work, the authors prove a stronger result, namely, that it is necessary and sufficient to stabilize only sixteen of the extreme plants. These sixteen plants are generated using the Kharitonov polynomials associated with the numerator and denominator. Furthermore, when additional information about the compensator is specified (sign of the gain and signs and relative magnitudes of the pole and zero), then, in some cases, it is necessary and sufficient to stabilize eight critical plants, while, in other cases, it is necessary and sufficient to stabilize twelve critical plants. >

Some discrete-time counterparts to Kharitonov's stability criterion for uncertain systems

In [1], Kharitonov gave an elegant and simple stability criterion for continuous-time systems. This note reports on similar results for discrete-time systems.

Experimental demonstration of reset control design

Abstract Using the describing function method, engineers in the 1950s and 1960s conceived of novel nonlinear compensators in an attempt to overcome performance limitations inherent in linear time-invariant (LTI) control systems. This paper is concerned with a subset of such devices called “reset controllers”, which are LTI systems equipped with mechanisms and laws to reset their states to zero. This paper reports on a design procedure and a laboratory experiment, the first to be reported in the literature, in which the resulting reset controller provides better design tradeoffs than LTI compensation. Specifically, it is shown that reset control increases the level of sensor-noise suppression without sacrificing either disturbance-rejection performance or gain/phase margins.