Fernando Paganini

Dynamics of TCP/RED and a scalable control

We demonstrate that the dynamic behavior of queue and average window is determined predominantly by the stability of TCP/RED, not by AIMD probing nor noise traffic. We develop a general multi-link multi-source model for TCP/RED and derive a local stability condition in the case of a single link with heterogeneous sources. We validate our model with simulations and illustrate the stability region of TCP/RED. These results suggest that TCP/RED becomes unstable when delay increases, or more strikingly, when link capacity increases. The analysis illustrates the difficulty of setting RED parameters to stabilize TCP: they can be tuned to improve stability, but only at the cost of large queues even when they are dynamically adjusted. Finally, we present a simple distributed congestion control algorithm that maintains stability for arbitrary network delay, capacity, load and topology.

FAST TCP: from theory to experiments

We describe a variant of TCP, called FAST, that can sustain high throughput and utilization at multigigabits per second over large distances. We present the motivation, review the background theory, summarize key features of FAST TCP, and report our first experimental results.

Analysis of implicitly defined systems

An alternative paradigm is considered for robustness analysis, where systems are described in implicit form. The central role in this formulation is played by equations rather than input-output maps. The framework for robust stability analysis is appropriately extended, and a necessary and sufficient condition is proved for the case of arbitrary structured norm bounded perturbations. Finally, the constant matrix version of this framework is considered, leading to an extension of the structured singular value /spl mu/; the corresponding upper bound theory is developed fully.<<ETX>>

Behavioral approach to robustness analysis

This paper introduces a general and powerful framework for modeling and analysis of uncertain systems. One immediate concrete result of this work is a practical method for computing robust performance in the presence of norm-bounded perturbations and both norm-bounded and white-noise disturbances.

Set descriptions of white noise and worst case induced norms

This paper provides a framework for analyzing white noise disturbances in linear systems. Rather than the usual stochastic approach, noise signals are described as elements in sets and the disturbance rejection properties of the system are described in a worst case setting. This type of modeling of noise and disturbances very much fits the philosophy of both the behavioral and robust control settings. The description is based on properties of finite records of signals, which may be verified directly on experimental data. Bounds of system gain for input signals in these sets are given, and their asymptotic behavior for long data records is analyzed.<<ETX>>

Interconnection of uncertain behavioral systems for robust control

This paper attempts to relate robust control and behavioral frameworks by incorporating structured uncertainty into the description of behavioral systems. Behavioral equations are expressed as linear fractional transformations (LFTs) on an uncertainty structure, and a method of interconnection is outlined. A method for obtaining input-output maps from LFT representations of behavioral systems is also presented. This extension of the behavioral framework is compatible with existing robust control methods, such as /spl mu/ analysis, which can be used to provide robustness test in behaviors. A simple example is presented that illustrates some of the issues which arise in this extension.<<ETX>>

A State-Space Theory of Uncertain Systems

Abstract This paper presents a tutorial summarizing recent work on generalizing standard state-space results such as stability and performance analysis, realization theory, stability and stabilization, and H ∞ optimal control to uncertain systems described by Linear Fractional Transformations (LFTs)

Necessary and sufficient conditions for robust H/sub 2/ performance

An exact condition is obtained for worst-case H/sub 2/ performance analysis of a system under structured uncertainty. This test is a convex feasibility condition across frequency, of the same nature and computational complexity as the corresponding conditions for H/sub /spl infin// performance.

Unifying robustness analysis and system ID

A unified systems analysis framework is presented, which includes conventional robustness analysis, model validation, and system identification as special cases and thus shows them to be instances of the same fundamental problem. A concrete version of this framework is developed for the linear case, based on a generalized structured singular value. This unification forms the basis for the use of common computational tools and and a more natural interplay between modeling, identification, and robustness analysis.<<ETX>>

Controller synthesis for implicitly defined uncertain systems

This paper builds on the previous work by the authors of providing a general framework for modeling and analysis of uncertain systems. This work centers on the use of implicit equations to characterize uncertain systems, in a manner consistent with the behavioral framework. We propose a method for synthesizing controllers for implicitly defined uncertain systems, which reduces to the so called D-K iteration procedure when the system can be written in explicit form. One immediate consequence of this work is a practical method for synthesizing controllers in the presence of norm bounded perturbations and both norm-bounded and white-noise disturbances, which encompasses the so called robust /spl Hscr//sub 2/ synthesis problem.<<ETX>>