Driss Boutat

Institut National des Sciences Appliquées Centre Val de Loire, Bourges, France · Control Team PRISME

In this paper, non-asymptotic and robust estimation for fractional integrals of noisy acceleration is considered for a class of fractional linear systems based on the study of the behaviour of fractional derivatives at zero. Particularly, the position and velocity can be estimated from the noisy acceleration via the designed estimators. Such estima...

In this paper, a class of fractional order vibration systems is considered, where the fractional differentiation orders are arbitrary real numbers between 0 and 2. The objective is to fast and robustly estimate the fractional integrals and derivatives of positions from noisy accelerations. In particular, the velocities and positions can be estimate...

This chapter provides a new geometric algorithm to overcome some obstructions that cannot be handled by those results proposed in Chaps. 3 and 4. This result is based on those presented in Chaps. 3 and 4, by adding an auxiliary dynamics into the studied nonlinear systems. Necessary and sufficient geometric conditions are deduced to guarantee the ex...

Till now, all the observer normal forms presented in Chaps. 3– 7 are focused on nonlinear dynamical systems with single output. The extension of the previous results to the case with multiple outputs is not trivial [3, 13]. The first attempt was made by [6, 10], and this chapter will firstly summarize their ideas, and then discuss the main differen...

This chapter aims at extending the differential geometric method to design observers for nonlinear singular dynamical systems. Singular systems widely exist in engineering systems, such as chemical system, biological system, electrical circuit and so on. These systems are governed by mixing differential and algebraic equations, which is the key dif...

This chapter firstly presents the pioneering work of Krener [6, 7], for the purpose of transforming a general nonlinear system into the so-called nonlinear observer normal form with output injection. As it has been already mentioned in Chap. 1, this form contains a linear part which is of Brunovsky’s canonical form, and a nonlinear part which is on...

Before dealing with the observer design for dynamical systems, we need firstly to analyze whether the states of the studied dynamical system can be observable or not. This property is named as observability in the literature. Therefore, this chapter aims at recalling the existing results on observability analysis approaches and observer design tech...

In the previous three chapters, the desired observer normal forms ( 3.3), ( 4.3) and ( 5.6) have the common point, i.e., the linear part is a constant matrix of Brunovsky form and the nonlinear part is a function of known (measured) variables. In this chapter, we enlarge the desired observer normal form by allowing output-depending matrix for its l...

In the previous chapters, we have applied differential geometric methodDifferential geometric method to design observers for nonlinear dynamical systems whose states are supposed to be fully observable. However, in practice some systems might be only partially observable, i.e., only a part of states are observable. For this topic, several works hav...

Through this book, we will adopt a geometric point of view to analyze nonlinear dynamical systems. Geometrically speaking, the behavior of a dynamical system can be governed by the associated vector field. In this sense, the dynamical behavior of such a system can be presented by smooth trajectories tangent to this vector field. Then, for a given d...

ForOutput diffeomorphism certainOutput injection nonlinear dynamical systemsObserver normal form with output injection, the geometric conditions provided in Chap. 3 might not be satisfied, because the desired observer normal form was imposed to have a linear output. This chapter aims at relaxing this constraint by proposing new geometric conditions...

This paper aims to fast and robustly estimate the fractional integrals and derivatives of positions from noisy accelerations for a class of fractional order vibration systems defined by the Caputo fractional derivative. The main idea is to convert the original issue into the estimation of the fractional integrals of accelerations and the ones of th...

This book presents a differential geometric method for designing nonlinear observers for multiple types of nonlinear systems, including single and multiple outputs, fully and partially observable systems, and regular and singular dynamical systems. It is an exposition of achievements in nonlinear observer normal forms. The book begins by discussin...

https://driss-boutat2019.medium.com/quantum-computing-first-steps-using-ibm-quantum-experience-f8d830f4f9b2

This paper aims to design model-free fractional order differentiators to non-asymptotically and robustly estimate both the Riemann-Liouville and Caputo fractional derivatives of an unknown signal from its discrete and noisy observation. To achieve this, new fractional integration by parts formulas are first introduced. Then, by applying the general...

https://driss-boutat2019.medium.com/gradient-field-in-optimization-169b5abd57f2

https://driss-boutat2019.medium.com/gradient-field-in-optimization-169b5abd57f2

https://driss-boutat2019.medium.com/matrices-eigenvectors-eigenvalues-9cd722561a57

https://driss-boutat2019.medium.com/build-equations-of-second-order-a73774dbf346

https://driss-boutat2019.medium.com/matrices-eigenvectors-eigenvalues-9cd722561a57

https://driss-boutat2019.medium.com/build-equations-of-second-order-a73774dbf346

This paper applies a numerical method of polynomial function approximation to the numerical analysis of variable fractional order viscoelastic rotating beam. First, the governing equation of the viscoelastic rotating beam is established based on the variable fractional model of the viscoelastic material. Second, shifted Bernstein polynomials and Le...

In this paper, an algebraic and robust fractional order differentiator is designed for a class of fractional order linear systems with an arbitrary differentiation order in [0,2]. It is designed to estimate the fractional derivative of the pseudo-state with an arbitrary differentiation order as well as the one of the output. In particular, it can a...

This work aims at developing a class of nonlinear dynamical systems that can be converted into nonlinear observer normal forms, which support the well-known high gain observer. This will be performed by means of the so-called dynamics extension method which explicitly supplies a set of auxiliary dynamics and changes of coordinates. In this work, th...

This paper aims to provide a set of criteria to ensure the stability or stabilization of a class of fractional order systems (FOS) for a given order α that belongs to the interval (0,2). These criteria are based on a unified structure of linear matrix inequalities (LMIs). Their add-value manifests in involving the least real decision variables of L...

I give a new way of thinking about the quadratic equation and thus solve easily and master the behavior of second order differential equations and build them from solutions.

My presentation is about some observer normal forms

It is well-known that observer design is a powerful tool to estimate the states of a dynamical system. Given a multi-output nonlinear dynamical system whose states are partially observable, this paper investigates the problem of observer design to estimate those observable states. It considers firstly a nonlinear system without inputs, and provides...

The aim of this paper is to design an algebraic fractional order differentiator for a class of commensurate fractional order linear systems modeled by the pseudo-state space representation. This differentiator is devoted to non-asymptotically and robustly estimating the fractional derivative of the output with an arbitrary order without knowing the...

The aim of this paper is to fast and robustly estimate the positions and velocities from the measured noisy accelerations for a class of dynamical systems modelled by a set of second order linear differential equations. The obtained estimators can be applied to a large number of on-line practical applications in noisy environment. For this purpose,...

We were delighted to receive Professor Leo CHUA at INSA CVL, who gave an excellent talk on "Five non-volatile memristor enigmas solved". A lot of Thanks Leo.

2019 International Conference on Fractional Calculus Theory and Applications (ICFCTA 2019) will be held in Bourges, France, from April 25 to April 30. The conference is co-sponsored by LE STUDIUM Loire Valley Institute for Advanced Studies (France), National Institute of Applied Sciences of Centre Val de Loire (France), Yanshan University (China) t...

Professor D. Boutat, Professor Y. Chen and Dr. D. Liu organized the 2019 International Conference on Fractional Calculus Theory and Applications (ICFCTA 2019) will be held in Bourges, France, from April 25 to April 30. The conference is co-sponsored by LE STUDIUM Loire Valley Institute for Advanced Studies (France), National Institute of Applied Sc...

Introduction to the quantum computing and IBM Q Experience Simulations.

In this paper, an efficient numerical technique based on the shifted Chebyshev polynomials (SCPs) is established to obtain numerical solutions of generalized fractional pantograph equations with variable coefficients. These polynomials are orthogonal and have compact support on [0,L]. We use these polynomials to approximate unknown solutions. Using...

Under environmental excitation and based on observability, an online model to predict the state of heavy-duty machine tool-foundation systems is proposed aimed to address the difficulties of directly measuring machine tool displacement states. The aim of the model is to address the difficulties associated with directly measuring machine tool displa...

In this paper, a non-asymptotic and robust method is proposed to estimate the fractional integral and derivative of the pseudo-state for a class of fractional order linear systems in noisy environment with unknown initial conditions. To the best of our knowledge, no method has been developed for such estimation. Firstly, the estimation problem is t...

In this article, we investigate numerical solution of a class of multi-order fractional di�erential equation with error correction and convergence analysis. According to fractional di�erential de�nition in Caputo's sense, fractional di�erential operator matrix is deduced. The problem is reduced to a set of algebraic equations and we apply MATLAB to...

This paper aims at non-asymptotically estimating the fractional integral and derivative of the pseudo-state for a class of fractional order linear systems in noisy environment with unknown initial conditions. For this purpose, the estimation problem is transformed to estimate the fractional integral and derivative of the output and a set of unknown...

In this paper, a non-asymptotic pseudo-state estimator for a class of commensurate fractional order linear systems is designed in noisy environment. Different from existing modulating functions methods, the proposed method is based on the system model with fractional sequential derivatives by introducing fractional order modulating functions. By ap...

In this paper, the global Mittag-Leffler stability issue of fractional-order neural networks (FNNs) with piecewise constant argument is investigated. Firstly, a new inequality with respect to the fractional derivative of integer-order variable upper limit integral is proposed, which not only is favorable to the construction of Lyapunov function but...

Abstract—Conventional active Incremental Structure from Motion (ISfM) schemes require a precise knowledge of the linear and angular velocities of the vision system to compute the 3D structure of the observed scene. Furthermore, they are generally coupled and non-linear which makes the reconstruction inaccurate. In this paper, we present a novel act...

The aim of this paper is to design an algebraic and robust fractional order differentiator to estimate both the Riemann-Liouville and the Caputo fractional derivatives with an arbitrary order of an unknown signal in noisy environment, without knowing the model defining the signal. For this purpose, a new class of fractional order Jacobi orthonormal...

This paper aims at designing a non-asymptotic fractional order differentiator for a class of fractional order linear systems with zero initial conditions, where the fractional orders can be commensurate or non commensurate, and the output is corrupted by a non zero-mean noise. Firstly, a set of fractional differential equations are constructed, bas...

This paper aims at designing a non-asymptotic fractional order differentiator for a class of fractional order linear systems with zero initial conditions, where the fractional orders can be commensurate or non-commensurate, and the output is corrupted by a non zero-mean noise. Firstly, a set of fractional differential equations are constructed, bas...

This paper investigates observer design problem for a large class of nonlinear singular systems with multi outputs. We firstly regularize the singular system by injecting the derivative of outputs into the system. Then differential geometric method is applied to transform the regularized system into a simple normal form, for which a Luenberger-like...

This paper presents a new approach to estimate states and parameters of the permanent magnet synchronous motor (PMSM) in the presence of unknown load torque disturbance. Indeed, it highlights an auxiliary dynamics that is added to the PMSM model. Thereby, it supplies a change of coordinates that transforms the extended model (PMSM model together wi...

This study presents a new approach to estimate states and parameters of the permanent magnet synchronous motor (PMSM) in the presence of unknown load torque disturbance. Indeed, it highlights an auxiliary dynamics that is added to the PMSM model. Thereby, it supplies a change of coordinates that transforms the extended model (PMSM model together wi...

This paper aims at designing a non-asymptotic fractional order differentiator for a class of fractional order linear systems to estimate the Riemann-Liouville fractional derivatives of the output in discrete noisy environment. The adopted method is a recent algebraic method originally introduced by Fliess and Sira-Ramirez. Firstly, the fractional d...

This paper investigates observer design problem for a large class of nonlinear singular systems with multi outputs. We firstly regularize the singular system by injecting the derivative of outputs into the system. Then differential geometric method is applied to transform the regularized system into a simple normal form, for which a Luenbergerlike...

The observer design for partial differential equations has so far been an open problem. In this paper, an observer design for systems with distributed parameters using sliding modes theory and backstepping-like procedure in order to achieve exponential convergence is presented. Such an observer is built using the knowledge available within and thro...

In this paper, we use Bernstein polynomials to seek the numerical solution of a class of nonlinear variable order fractional differential equation. The fractional derivative is described in the Caputo sense. Three different kinds of operational matrixes with Bernstein polynomials are derived and are utilized to transform the initial equation into t...

This paper aims at extending the modulating functions method to design a non-asymptotic and robust pseudo-state estimator for a class of fractional order linear systems which can be transformed into the Brunovsky’s observable canonical form of pseudo-state space representation with zero initial conditions. For this purpose, the former form is first...

In this paper, we investigate the problem of simultaneous state and parameter estimation for a class of nonlinear systems which can be transformed into an output depending normal form. A new and simple adaptive observer for such class of systems is presented. Sufficient condition for the existence of the proposed observer is derived. A concrete app...

This paper aims at designing a non-asymptotic and robust pseudo-state estimator for a class of fractional order linear systems which can be transformed into the Brunovsky’s observable canonical form of pseudo-state space representation with unknown initial conditions. Firstly, this form is expressed by a fractional order linear differential equatio...

There is a wide body of scientific literature on the well-known Predator-Prey ecological models. However, just a few number of published articles deal with the problem of observer design for these dynamical systems. The aim of this paper is to apply the nonlinear observer normal forms to address this problem. We first introduce the notion of nonlin...

In this paper, we investigate the estimation problem for a class of partially observable nonlinear systems. For the proposed Partial Observer Normal Form (PONF), necessary and sufficient conditions are deduced to guarantee the existence of a change of coordinates which can transform the studied system into the proposed PONF. Examples are provided t...

In this paper, a numerical method is proposed to estimate the variable-order fractional derivatives of an unknown signal in noisy environment. Firstly, the wavelet denoising process is adopted to reduce the noise effect for the signal. Secondly, polynomials are constructed to fit the denoised signal in a set of overlapped subintervals of a consider...

The paper presents an observer synthesis method for distributed parameter systems using the transformation bakstepping. The Backstepping method transforms the system into a stable system with a simpler structure. The method is applied to a chemical reactor tube

This paper aims at designing a fractional order differentiator based on a integer order linear system with zero initial conditions, where the fractional derivatives of the output are estimated using the output observation corrupted by a non zero-mean noise. Firstly, an integral algebraic formula for the fractional derivatives of the output is exact...

This paper deals with the problem to estimate some states of a multi-output nonlinear dynamical system which is partially observable. To address this problem, this paper provides a set of geometrical conditions that guarantee the existence of a change of coordinates which decomposes the studied nonlinear dynamical system into two dynamical subsyste...

Susceptible Exposed Infectious and Recovered epidemic model endowed with a treat- ment function (SEIR-T model) is a well-known model used to reproduce the behavior of an epidemic, where the susceptible population and the exposed population need to be estimated to predict and control the propagation of a contagious disease. This paper fo- cuses on t...

This paper aims at estimating the Caputo fractional derivatives for a class of signals satisfying a linear differential equation. For this purpose, an estimator for the initial conditions of the studied signal and an fractional order differentiator for the Riemann-Liouville fractional derivatives are needed. Firstly, an algebraic integral formula f...

This paper aims to study the existence of a change of coordinates which permits to transform a class of nonlinear dynamical systems into the so-called nonlinear observer canonical form. Moreover, an algorithm used to construct such a change of coordinates is given. Based on this form, we can design an observer with a linear error dynamic. This pape...

In this paper, we design exponentially convergent observer for the systems with distributed parameters. A Volterra integral transformation is used to change the coordinates of the error dynamics into exponentially stable target systems using the backstepping procedure. The gains of the observer, which are attained by solving a Partial Differential...

This paper aims at designing a digital fractional order differentiator for a class of signals satisfying a linear differential equation to estimate fractional derivatives with an arbitrary order in noisy case, where the input can be unknown or known with noises. Firstly, an integer order differentiator for the input is constructed using a truncated...