Event-triggered gain scheduling of reaction-diffusion PDEs

This paper deals with the problem of boundary stabilization of 1D reaction-diffusion PDEs with a time- and space- varying reaction coefficient. The boundary control design relies on the backstepping approach. The gains of the boundary control are scheduled under two suitable event-triggered mechanisms. More precisely, gains are computed/updated on events according to two state-dependent event-triggering conditions: static-based and dynamic-based conditions, under which, the Zeno behavior is avoided and well-posedness as well as exponential stability of the closed-loop system are guaranteed. Numerical simulations are presented to illustrate the results.Comment: 20 pages, 5 figures, submitted to SICO

On local finite-time stabilization of the Viscous Burgers equation via boundary switched linear feedback

International audienceThis paper considers the problem of local finite-time stabilization of the viscous Burgers equation. A boundary switched linear control with state dependent switching law is designed based on the Backstepping approach. The strategy builds on discontinuous kernels which render the control function a piecewise continuous one. It is proved that such a control stabilizes locally the viscous Burgers equation and that the settling time depends on initial conditions. A simulation result is provided to validate the theoretical results

Estabilidad de sistemas eléctricos de potencia mediante técnicas de comutación en sistemas de transmisión

This article presents an optimization problem, where an Optimal Power Flow (OPF) will be applied, which will include the switching techniques, focused on the stability of busbar voltages in the transmission system. The transmission commutation is a technique that can bring various benefits to the system as economic, technical and mainly maintaining the continuity of the electric service. Using a nonlinear programming model (NLP) using the General Algebraic Modeling System (GAMS), this will work on the IEEE 14 Bar model and in conjunction with the DigSilent program the different tests and comparisons of the data acquired. In conjunction with the study the stability indexes will be able to obtain better results in the part of stability of voltage. The results obtained from the present investigation solved the problems posed, where the switching techniques serve correctly against outputs of transmission lines, respecting the voltages p.u. in the operational margin, reducing the losses of the system and thus have a safe, efficient and reliable system.En este artículo se presenta un problema de optimización, donde se aplicará un Flujo Óptimo de Potencia (OPF) que incluirá las técnicas de conmutación, enfocado en la estabilidad de voltajes de las barras en el sistema de transmisión. La conmutación de transmisión es una técnica la cual podrá traer diversos beneficios al sistema como económicos, técnicos y principalmente manteniendo la continuidad del servicio eléctrico. Utilizando un modelo de programación no lineal (NLP) mediante el manejo del General Algebraic Modeling System (GAMS), para ello se trabajará en el modelo de las 14 Barras del IEEE y conjuntamente con el programa DigSilent se realizará las distintas pruebas y comparaciones de los datos adquiridos. Conjuntamente con el estudio los índices de estabilidad se podrán obtener mejores resultados en la parte de estabilidad de voltaje. Los resultados logrados de la presente investigación solucionó los problemas planteados, donde las técnicas de conmutación sirven correctamente frente a salidas de líneas de transmisión, respetando los voltajes p.u. en el margen operativo, reduciendo las pérdidas del sistema y así tener un sistema seguro, eficiente y confiable

Switching rules for stabilization of linear systems of conservation laws

International audienceIn this paper, the exponential convergence in L 2-norm is analyzed for a class of switched linear systems of conservation laws. The boundary conditions are subject to switches. We investigate the problem of synthesizing stabilizing switching controllers. By means of Lyapunov techniques, three control strategies are developed based on steepest descent selection, possibly combined with a hysteresis and a low-pass filter. For the first strategy we show the global exponential stabilizability, but no result for the existence and uniqueness of trajectories can be stated. For the other ones, the problem is shown to be well posed and global exponential convergence can be obtained. Moreover, we consider the robustness issues for these switching rules in presence of measurement noise. Some numerical examples illustrate our approach and show the merits of the proposed strategies. Particularly, we have developped a model for a network of open channels, with switching controllers in the gate operations

An optimisation approach for stability analysis and controller synthesis of linear hyperbolic systems

International audienceIn this paper, we consider the problems of stability analysis and control synthesis for first-order hyperbolic linear Partial Differential Equations (PDEs) over a bounded interval with spatially varying coefficients. We propose Linear Matrix Inequalities (LMI) conditions for the stability and for the design of boundary and distributed control for the system. These conditions involve an infinite number of LMI to solve. Hence, we show how to overapproximate these constraints using polytopic embeddings to reduce the problem to a finite number of LMI. We show the effectiveness of the overapproximation with several examples and with the Saint-Venant equations with friction

Event-based control of linear hyperbolic systems of conservation laws

International audienceIn this article, we introduce event-based boundary controls for 1-dimensional linear hyperbolic systems of conservation laws. Inspired by event-triggered controls developed for finite-dimensional systems, an extension to the infinite dimensional case by means of Lyapunov techniques, is studied. The main contribution of the paper lies in the definition of two event-triggering conditions, by which global exponential stability and well-posedness of the system under investigation is achieved. Some numerical simulations are performed for the control of a system describing traffic flow on a roundabout

Stability of switched linear hyperbolic systems by Lyapunov techniques (full version)

Switched linear hyperbolic partial differential equations are considered in this paper. They model infinite dimensional systems of conservation laws and balance laws, which are potentially affected by a distributed source or sink term. The dynamics and the boundary conditions are subject to abrupt changes given by a switching signal, modeled as a piecewise constant function and possibly a dwell time. By means of Lyapunov techniques some sufficient conditions are obtained for the exponential stability of the switching system, uniformly for all switching signals. Different cases are considered with or without a dwell time assumption on the switching signals, and on the number of positive characteristic velocities (which may also depend on the switching signal). Some numerical simulations are also given to illustrate some main results, and to motivate this study