control based on saturated time-delay systems theory of mach number in wind tunnels

Producción CientíficaA proposal for the regulation of the Mach number in wind tunnels using static state feedback for saturated systems with delays is presented here. As these systems can be precisely represented by a time-delay model with saturating inputs, a general solution for discrete delayed systems with saturating input is first derived. This general solution is based on modeling the saturation using a Lyapunov functional, using free weighting matrices and maximizing the set of admissible initial conditions. The application of this solution to the control of the Mach number in a wind tunnel is then presented, illustrating the design procedures.MiCInn Project DPI2014-54530-

congestion control of data network by using anti-windup approach

Producción CientíficaAn Active Queue Management (AQM) scheme is design to control congestion in data networks, which includes anti-windup to deal with control signal saturation. More precisely, a methodology is proposed to design advanced AQM systems capable of regulating queue size even in the presence of significant disturbances. Hence, we first provide sufficient conditions for stabilization for the equivalent class of systems, which are derived in terms of LMI: this makes possible to derive optimization solutions that ensure performance and stability for a large domain of initial conditions. This approach is validated with a numerical example that illustrates the methodology, and the improvements with respect to previous congestion control solutions

A two dimensional fluid model for TCP/AQM analysis

This work proposes a new mathematical model for the TCP/AQM system that aims to improve the accuracy of existing fluid models, especially with respect to the sequential events that occur in the network. The analysis is based on the consideration of two time bases, one at the queue's router level and the other at the congestion window level, which leads to the derivation of a new nonlinear two-dimensional fluid model for Internet congestion control. To avoid the difficult task of assessing stability of a 2D nonlinear dynamic model, we perform a local stability analysis of a 2D linear TCP AQM model. By constructing a new two dimensional second order Bessel Legendre Lyapunov functional, new matrix inequalities are derived to evaluate the stability of the 0-input system and to synthesize a feedback controller. Finally, two Internet traffic scenarios, with state space matrices for replicability, are presented, demonstrating the validity of the theoretical results.Comment: Active queue management, network assisted congestion control, TCP/AQM, 2D time delay systems, Roesser model, 2D second order bessel Legendre, Lyapuno

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

Finite-Time Stability for Discrete-Time Systems with Time-Varying Delays and Nonlinear Perturbations Using Relaxed Summation Inequality

Producción CientíficaThis article deals with the problem of delay-dependent finite-time stability (FTS) for delayed discrete-time systems with nonlinear perturbations. First, based on a Lyapunov–Krasovskii Functional, delay-dependent FTS conditions are provided by introducing some free-weighting matrices. Then, a new reduced free-matrix-based inequality is established to estimate the single summation term. The dimensions of these free matrices integral in our results are less than those obtained in the literature. This reduction in the number of variables does not mean that our method is a particular case but simply that our approach is completely different from the others and therefore our method is more effective. Thus, less conservative design conditions are obtained in this paper in terms of linear matrix inequalities (LMIs) and solved using MATLAB’s LMI toolbox to achieve the desired performance. The purpose of this paper is to derive sufficient conditions that ensure the finite-time stability of the discrete-time system. Finally, numerical examples are examined to show the advantage and effectiveness of the proposed results.MICInn, PID2021-123654OB-C31MICInn, PID2020-112871RB-C2

multiclass aQM on a tCP/IP router: a control theory approach

Producción CientíficaActive queue management (AQM) is a well-known technique to improve routing performance under congested traffic conditions. It is often deployed to regulate queue sizes, thus aiming for constant transmission delay. This work addresses AQM using an approach based on control theory ideas. Compared with previous results in the literature, the novelty is the consideration of heterogeneous traffic, ie, multiclass traffic. Thus, each traffic class may have different discarding policies, queue sizes, and bandwidth share. This feature brings the proposal nearer to real network management demands than previous approaches in the literature. The proposed technique assumes that each class already has a simple controller, designed a priori, and focuses on designing a static state-feedback controller for the multiclass system, where the design is based on using LMIs for the calculations. For this, optimization problems with LMI constraints are proposed to compute the state-feedback gains that ensure stability for a large set of admissible initial conditions. These conditions ensure not only closed-loop stability but also some level of performance. As far as we know, this is the first control theory based approach for the AQM problem on TCP/IP routers that allows a multiclass AQM while also considering time-varying delays and input saturation. This is an important step to frame AQM in a more formal, yet realistic context, enabling it to address important service level agreement (SLA) directives. The proposal is tested on a simulated system at the end of this paper, showing the feasibility and performance of the approach in the presence of multiclass traffic.Junta de Castilla y León y FEDER. Grant Numbers: CLU 2017-09, UIC 23

robust stabilization using a sampled-data strategy of uncertain neutral state-delayed systems subject to input limitations

Producción CientíficaStabilization of neutral systems with state delay is considered in the presence of uncertainty and input limitations in magnitude. The proposed solution is based on simultaneously characterizing a set of stabilizing controllers and the associated admissible initial conditions through the use of a free weighting matrix approach. From this mathematical characterization, state feedback gains that ensure a large set of admissible initial conditions are calculated by solving an optimization problem with LMI constraints. Some examples are presented to compare the results with previous approaches in the literature.MICINnn DPI2014-54530-

Stabilization of Delta Operator Systems with Actuator Saturation via an Anti-Windup Compensator

The design of an anti-windup controller for delta operator systems with time-varying delay and actuator saturation is addressed. By utilizing the input-output approach and three-term approximation, we first transform the original system into two equivalent interconnected subsystems. Then, by employing the scaled small-gain theorem, the Lyapunov–Krasovskii functional, and Wirtinger’s integral inequality, sufficient conditions for the synthesis of an anti-windup compensator are presented in the form of linear matrix inequalities (LMIs). The estimated domain of attraction is maximized by an optimization algorithm. Numerical examples are studied to show the merits of the proposed technique

Control of Discrete 2-D Takagi–Sugeno Systems via a Sum-of-Squares Approach

Producción CientíficaThe stabilization of Takagi–Sugeno systems is solved here for the two-dimensional polynomial discrete case, by using the sum-of-squares approach. First, we provide a stabilization condition formulated in terms of polynomial multiple Lyapunov functions. Then, a non-quadratic stabilization condition is developed by applying relaxed stabilization technique. Both conditions can be used for design, by solving them using numerical tools such as SOSTOOLS. A numerical example illustrates the effectiveness of the results.Junta de Castilla y León y EU-FEDER (CLU 2017-09) y (UIC 233)Secretaría de Estado de Investigación, Desarrollo e Innovación (Grant. DPI2014-54530-R

Delay Dependent Exponential Stability and Guaranteed Cost of Time-Varying Delay Singular Systems

This paper deals with the problem of delay-dependent guaranteed cost exponential stability of singular systems with time-varying delay. Some improved delaydependent conditions are presented, in the form of linear matrix inequalities to ensure the considered system to be regular, impulse free and exponentially stable with the existence of a guaranteed cost. Numerical examples are given to show the usefulness of the proposed results