Quasi-optimal robust stabilization of control systems

In this paper, we investigate the problem of semi-global minimal time robust stabilization of analytic control systems with controls entering linearly, by means of a hybrid state feedback law. It is shown that, in the absence of minimal time singular trajectories, the solutions of the closed-loop system converge to the origin in quasi minimal time (for a given bound on the controller) with a robustness property with respect to small measurement noise, external disturbances and actuator noise

D1-Input-to-State Stability of a Time-Varying Nonhomogeneous Diffusive Equation Subject to Boundary Disturbances

International audienceD1-Input-to-state stability (D1ISS) of a diffusive equation with Dirichlet boundary conditions is shown, in the L2-norm, with respect to boundary disturbances. In particular, the spatially distributed diffusion coefficients are allowed to be time-varying within a given set, without imposing any constraints on their rate of variation. Based on a strict Lyapunov function for the system with homogeneous boundary conditions, D1ISS inequalities are derived for the disturbed equation. A heuristic method used to numerically compute weighting functions is discussed. Numerical simulations are presented and discussed to illustrate the implementation of the theoretical results

Dynamic Boundary Stabilization of First Order Hyperbolic Systems

International audienceIn this chapter, we address the problem of the dynamic boundary stabilization of linear, quasilinear and LPV first-order hyperbolic systems. We provide sufficient conditions for the exponential stability for this class of infinite dimensional systems by means of Lyapunov based techniques and matrix inequalities. We develop an applicative example of a temperature boundary control in a Poiseuille flow using some of our main results and we present simulation results that illustrate the efficiency of our approach

Boundary Observers for Linear and Quasi-linear Hyperbolic Systems with Application to Flow Control

International audienceIn this paper we consider the problem of boundary observer design for one-dimensional fi rst order linear and quasi-linear strict hyperbolic systems with n rightward convecting transport PDEs. By means of Lyapunov based techniques, we derive some su fficient conditions for exponential boundary observer design using only the information from the boundary control and the boundary conditions. We consider static as well as dynamic boundary controls for the boundary observer design. The main results are illustrated on the model of an inviscid incompressible flow

A Strict Control Lyapunov Function for a Diffusion Equation with Time-Varying Distributed Coefficients

International audienceIn this paper, a strict Lyapunov function is developed in order to show the exponential stability and input-to-state stability (ISS) properties of a diffusion equation for nonhomogeneous media. Such media can involve rapidly time-varying distributed diffusivity coefficients. Based on this Lyapunov function, a control law is derived to preserve the ISS properties of the system and improve its performance. A robustness analysis with respect to disturbances and estimation errors in the distributed parameters is performed on the system, precisely showing the impact of the controller on the rate of convergence and ISS gains. This is important in light of a possible implementation of the control since, in most cases, diffusion coefficient estimates involve a high degree of uncertainty. An application to the safety factor profile control for the Tore Supra tokamak illustrates and motivates the theoretical results. A constrained control law (incorporating nonlinear shape constraints in the actuation profiles) is designed to behave as closely as possible to the unconstrained version, albeit with the equivalent of a variable gain. Finally, the proposed control laws are tested under simulation, first in the nominal case and then using a model of Tore Supra dynamics, where they show adequate performance and robustness with respect to disturbances

Bayesian calibration of an avalanche model from autocorrelated measurements along the flow: application to velocities extracted from photogrammetric images

International audiencePhysically-based avalanche propagation models must still be locally calibrated to provide robust predictions, e.g. in long-term forecasting and subsequent risk assessment. Friction parameters cannot be measured directly and need to be estimated from observations. Rich and diverse data are now increasingly available from test-sites, but for measurements made along flow propagation, potential autocorrelation should be explicitly accounted for. To this aim, this work proposes a comprehensive Bayesian calibration and statistical model selection framework. As a proof of concept, the framework was applied to an avalanche sliding block model with the standard Voellmy friction law and high rate photogrammetric images. An avalanche released at the Lautaret test-site and a synthetic data set based on the avalanche are used to test the approach and to illustrate its benefits. Results demonstrate (1) the efficiency of the proposed calibration scheme, and (2) that including autocorrelation in the statistical modelling definitely improves the accuracy of both parameter estimation and velocity predictions. Our approach could be extended without loss of generality to the calibration of any avalanche dynamics model from any type of measurement stemming from the same avalanche flow

The Oncogenic EWS-FLI1 Protein Binds In Vivo GGAA Microsatellite Sequences with Potential Transcriptional Activation Function

The fusion between EWS and ETS family members is a key oncogenic event in Ewing tumors and important EWS-FLI1 target genes have been identified. However, until now, the search for EWS-FLI1 targets has been limited to promoter regions and no genome-wide comprehensive analysis of in vivo EWS-FLI1 binding sites has been undertaken. Using a ChIP-Seq approach to investigate EWS-FLI1-bound DNA sequences in two Ewing cell lines, we show that this chimeric transcription factor preferentially binds two types of sequences including consensus ETS motifs and microsatellite sequences. Most bound sites are found outside promoter regions. Microsatellites containing more than 9 GGAA repeats are very significantly enriched in EWS-FLI1 immunoprecipitates. Moreover, in reporter gene experiments, the transcription activation is highly dependent upon the number of repeats that are included in the construct. Importantly, in vivo EWS-FLI1-bound microsatellites are significantly associated with EWS-FLI1-driven gene activation. Put together, these results point out the likely contribution of microsatellite elements to long-distance transcription regulation and to oncogenesis