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State-feedback with memory for controlled positivity with application to congestion control

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Abstract

The problem of designing controllers for systems with delays, such that the closed-loop system is positive, stable and fulfils bounds on the system variables, is studied. In order to design this type of controller, a technique is provided, which is based on solving linear programming problems, as this allows the controllers that fulfil these properties to be easily characterised even in the presence of uncertainty in the plant description. Thus, these controllers ensure that the states are kept non-negative and that they fulfil limitations on the control and states. The work is completed with numerical simulations of the application of the methodology for router congestion control in computer networks, based on the synthesis of an active queue management system, thus demonstrating the usefulness of the proposed technique for practical problems.

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... Because of the existence of positive constraints in the switched systems, numerous results from the study on normal switched systems may not be applicable to SPSs. Besides, several phenomena can be modeled by SPSs, such as compartmental model [30], water-quality model [31], formation flying [32], congestion control [33], wireless power control [34], and network communication using transmission control protocol [35]. Due to the complex dynamics of SPSs and their numerous applications, stability analysis on SPSs has been a significant investigation, and some relevant researches have been reported in [36][37][38][39][40][41][42][43][44]. ...
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Stability and robust stability of time-delay systems: A guided tour.- Convex directions for stable polynomials and quasipolynomials: A survey of recent results.- Delay-independent stability of linear neutral systems: A riccati equation approach.- Robust stability and stabilization of time-delay systems via integral quadratic constraint approach.- Graphical test for robust stability with distributed delayed feedback.- Numerics of the stability exponent and eigenvalue abscissas of a matrix delay system.- Moving averages for periodic delay differential and difference equations.- On rational stabilizing controllers for interval delay systems.- Stabilization of linear and nonlinear systems with time delay.- Nonlinear delay systems: Tools for a quantitative approach to stabilization.- Output feedback stabilization of linear time-delay systems.- Robust control of systems with a single input lag.- Robust guaranteed cost control for uncertain linear time-delay systems.- Local stabilization of continuous-time delay systems with bounded inputs.
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This paper presents two alternative realisations for two-degrees-of-freedom (2-DOF) compensators. The characterisation of 1-DOF and 2-DOF compensators is first presented in terms of the set of allowable designs: the advantages of a 2-DOF compensator over a 1-DOF are also reviewed. Despite these advantages, 2-DOF compensators are not used as expected. One possible reason being the lack of design methodologies for such compensators. This may be the reason the different approaches found in the literature on 2-DOF compensator design are mainly based on optimisation procedures. The principal aim of the paper is to provide a framework for 2-DOF design where well-known classical design methods apply. Two design examples are presented. The first one presents a PID-based 2-DOF compensator to show the application of the realisation in a classical setting. The second example shows how the step response of an existing feedback controller can be improved
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Virtual Queue-based marking schemes have been recently proposed for AQM (Active Queue Management) in Internet routers. We consider a particular scheme, which we call the Adaptive Virtual Queue (AVQ), and study its following properties: stability in the presence of feedback delays, its ability to maintain small queue lengths and its robustness in the presence of extremely short flows (the so-called web mice). Using a mathematical tool motivated by the earlier work of Hollot et al, we present a simple rule to design the parameters of the AVQ algorithm. We then compare its performance through simulation with several well-known AQM schemes such as RED, REM, PI controller and a non-adaptive virtual queue algorithm. With a view towards implementation, we show that AVQ can be implemented as a simple token bucket using only a few lines of code. 1
Memoryless control of delayed systems in continuous time, to impose non-negative closed-loop states
  • M A Tadeo
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