Jean Pierre Barbot

Sliding Mode Control in Engineering

Introduction - an overview of classical sliding mode control differential inclusions and sliding mode control high-order sliding modes sliding mode observers dynamic sliding mode control and output feedback sliding modes, passivity, andflatness stability and stabilization discretization issues adaptive and sliding mode control steady modes in relay systems with delay sliding mode control for systems wiht time delay sliding mode control for systems with time delay sliding modecontrol of infinite-dimensional systems.

Compressive Sensing With Chaotic Sequence

Compressive sensing is a new methodology to capture signals at sub-Nyquist rate. To guarantee exact recovery from compressed measurements, one should choose specific matrix, which satisfies the Restricted Isometry Property (RIP), to implement the sensing procedure. In this letter, we propose to construct the sensing matrix with chaotic sequence following a trivial method and prove that with overwhelming probability, the RIP of this kind of matrix is guaranteed. Meanwhile, its experimental comparisons with Gaussian random matrix, Bernoulli random matrix and sparse matrix are carried out and show that the performances among these sensing matrix are almost equal.

SLIDING MODE OBSERVER FOR TRIANGULAR INPUT HYBRID SYSTEM

Abstract In this paper a methodology to design an observer for a class of hybrid nonlinear systems with no continuous state reset is proposed. By using hybrid systems techniques for modelling and synthesis, we propose a solution to the challenging observer problem related to such system. Some simulations illustrate the proposed approach.

Synchronous motor observability study and an improved zero-speed position estimation design

This paper deals with the Permanent Magnet Synchronous Motor (PMSM) observability analysis for sensorless control design. The problem of loss of observability at low frequency range is always recognized in experimental settings. Nevertheless, there are no sufficient theoretical observability analyses for the PMSM. In the literature, only the sufficient observability condition has been presented. Therefore, the current work is aimed especially to the necessary observability condition analysis. Furthermore, an Estimator/Observer Swapping system is designed here for the surface Permanent Magnet SynchronousMotor (PMSM) to overcome position observability problems at zero speed which is an unobservable state point.

Chaos in automatic control

OPEN-LOOP ANALYSIS Bifurcation and Chaos in Discrete Models: An Introductory Survey C. Mira Tools for Ordinary Differential Equations Analysis W. Perruquetti Normal Forms and Bifurcations of Vector Fields C. Dang Vu-Delcarte Feedback Equivalence of Nonlinear Control Systems: A Survey on Formal Approach W. Respondek and I.A. Tall Singular Perturbation and Chaos M. Djemai and S. Ramdani CLOSED-LOOP DESIGN Control of Chaotic and Hyperchaotic Systems L. Laval Polytopic Observers for Synchronization of Chaotic Maps G. Millerioux and J. Daafouz Normal Forms of Nonlinear Control Systems W. Kang and A.J. Krener Observability Bifurcations: Application to Cryptography J-P. Barbot, I. Belmouhoub, and L. Boutat-Baddas Nonlinear Observer Design for Smooth Systems A.J. Krener and M. Xiao SOME APPLICATIONS Chaos and Communications R. Quere, J. Guittard, and J.C. Nallatamby Chaos, Optical Systems, and Application to Cryptography L. Larger Indirect Field-Oriented Control of Induction Motors: A Hopf Bifurcation Analysis F. Gordillo, F. Salas, R. Ortega, and J. Aracil Implementation of the Chuas Circuit and its Application in the Data Transmission L. Boutat-Baddas, J-P. Barbot, and R. Tauleigne Synchronization of Discrete-Time Chaotic Systems for Secured Data Transmission I. Belmouhoub and M. Djemai Appendix A. On Ergodic Theory of Chaos INDEX

Observability analysis of PMSM

The current problems to successfully apply sensorless control techniques for Permanent Magnet Synchronous Motor (PMSM) are the existence of operating conditions for which the observer performance is remarkably deteriorated. This is due to difficulties in estimating correctly the rotor position at low speed. The failure of sensor-less schemes in some particular operating conditions has been always recognized in experimental settings. However, there are no sufficient theoretical observability analysis for the PMSM. In the literature, only the sufficient observability condition has been presented. Therefore, the current work is aimed specially to necessary observability condition analysis. Thus, we give here the necessary and sufficient states observability condition for the PMSM. An example is presented to illustrate the results.

Model based Bayesian compressive sensing via Local Beta Process

In the framework of Compressive Sensing (CS), the inherent structures underlying sparsity patterns can be exploited to promote the reconstruction accuracy and robustness. And this consideration results in a new extension for CS, called model based CS. In this paper, we propose a general statistical framework for model based CS, where both sparsity and structure priors are considered simultaneously. By exploiting the Latent Variable Analysis (LVA), a sparse signal is split into weight variables representing values of elements and latent variables indicating labels of elements. Then the Gamma-Gaussian model is exploited to describe weight variables to induce sparsity, while the beta process is assumed on each of the local clusters to describe inherent structures. Since the complete model is an extension of Bayesian CS and the process is for local properties, it is called Model based Bayesian CS via Local Beta Process (MBCS-LBP). Moreover, the beta process is a Bayesian conjugate prior to the Bernoulli Process, as well as the Gamma to Gaussian distribution, thus it allows for an analytical posterior inference through a variational Bayes inference algorithm and hence leads to a deterministic VB-EM iterative algorithm. HighlightsThis paper is dealing with the recovery problem for model based compressive sensing.This paper has proposed a hierarchical Bayesian model to describe the model based compressive sensing.Local Beta Process has been applied to describe the inherent structures of the sparse signals.Variational Bayesian approach has been exploited to implement the Bayesian inference.

Bayesian Compressive Sensing for clustered sparse signals

In traditional framework of Compressive Sensing (CS), only sparse prior on the property of signals in time or frequency domain is adopted to guarantee the exact inverse recovery. Besides sparse prior, cluster prior is introduced in this paper in order to investigate a class of structural sparse signals, called clustered sparse signals. A hierarchical statistical model is employed via Bayesian approach to model both the sparse prior and cluster prior and Markov Chain Monte Carlo (MCMC) sampling is implemented for the inference. Unlike the state-of-the-art algorithms based on the cluster prior, the proposed algorithm solves the inverse problem without any prior knowledge of the cluster parameters, even without the knowledge of the sparsity. The experimental results show that the proposed algorithm outperforms many state-of-the-art algorithms.

Chaotic synchronisation and secure communication via sliding-mode and impulsive observers

This paper addresses the design of a secure data transmission based on the synchronisation of two chaotic systems, with the use of unknown-input observers. The approach proposed here enhances the security level against intruders thanks to an intricate encryption system. It is shown also that this approach provides more robustness with respect to channel noise. The main feature consists in separating the encryption and synchronisation operations by using two coupled continuous chaotic systems in the transmitter. Technically, the scheme is based on impulsive and sliding mode unknown-input observers. This offers the advantage of estimating the (master) states and of reconstructing the unknown inputs simultaneously. The performances of the proposed method are highlighted by simulation results.

Delay estimation algorithm for nonlinear time-delay systems with unknown inputs

The theory of non-commutative rings allows determining whether or not there exists an equation called algebraically essential in order to estimate the delay on a nonlinear system. In this paper, it firstly recalls some literature results on algebraically essential equation. Then it is shown that this equation is generally not enough to guarantee the delay estimation, thus the notion of persistent signal with respect to delay estimation is introduced. Furthermore, based on the definitions of algebraically essential equation and of persistent signal, a delay estimation algorithm is proposed. Some simulation results have been presented in order to highlight the robustness (with respect to measurement noise) of the proposed algorithm.