Michel Fliess

Numerical differentiation with annihilators in noisy environment

Numerical differentiation in noisy environment is revised through an algebraic approach. For each given order, an explicit formula yielding a pointwise derivative estimation is derived, using elementary differential algebraic operations. These expressions are composed of iterated integrals of the noisy observation signal. We show in particular that the introduction of delayed estimates affords significant improvement. An implementation in terms of a classical finite impulse response (FIR) digital filter is given. Several simulation results are presented.

Model-free control

‘Model-free control’and the corresponding ‘intelligent’ PID controllers (iPIDs), which already had many successful concrete applications, are presented here for the first time in an unified manner, where the new advances are taken into account. The basics of model-free control is now employing some old functional analysis and some elementary differential algebra. The estimation techniques become quite straightforward via a recent online parameter identification approach. The importance of iPIs and especially of iPs is deduced from the presence of friction. The strange industrial ubiquity of classic PIDs and the great difficulty for tuning them in complex situations is deduced, via an elementary sampling, from their connections with iPIDs. Several numerical simulations are presented which include some infinite-dimensional systems. They demonstrate not only the power of our intelligent controllers but also the great simplicity for tuning them.

MODEL-FREE CONTROL AND INTELLIGENT PID CONTROLLERS: TOWARDS A POSSIBLE TRIVIALIZATION OF NONLINEAR CONTROL?

We are introducing a model-free control and a control with a restricted model for finite-dimensional complex systems. This control design may be viewed as a contribution to intelligent PID controllers, the tuning of which becomes quite straightforward, even with highly nonlinear and/or time-varying systems. Our main tool is a newly developed numerical differentiation. Differential algebra provides the theoretical framework. Our approach is validated by several numerical experiments.

Intelligent PID controllers

Intelligent PID controllers, or i-PID controllers, are PID controllers where the unknown parts of the plant, which might be highly nonlinear and/or time-varying, are taken into account without any modeling procedure. Our main tool is an online numerical differentiator, which is based on easily implementable fast estimation and identification techniques. Several numerical experiments demonstrate the efficiency of our method when compared to more classic PID regulators.

Robust residual generation for linear fault diagnosis: an algebraic setting with examples

We are generating residuals for linear fault diagnosis and isolation which are 1. robust with respect to a large variety of additive disturbances, u2009A reader who is already familiar with this algebraic setting may directly proceed to §u20093. The numerous examples on various aspects of diagnosis, like the previous one, are written on the other hand in such a way that they may be understood by anyone who is not mastering those mathematical tools. We hope therefore that our results might be understood by a large community. 2. working in closed-loop, even with uncertain parameters. Several examples with their computer simulations, including a concrete case-study of a two mass system, are enlightening our viewpoint. Our methods, which are mainly of algebraic flavour (module theory, differential algebra, and operational calculus), are borrowed from recent works on control and identification.

An algebraic framework for the design of nonlinear observers with unknown inputs

The observability properties of nonlinear systems with unknown inputs are characterized via differentially algebraic techniques. State variables and unknown inputs are estimated thanks to a new algebraic numerical differentiator. It is shown through an academic example and a concrete case-study that the proposed scheme can be applied to systems that fail to fulfill some usual structural assumptions.

On the output feedback control of a synchronous generator

In this article, we propose an output feedback regulation scheme for the electrical angle trajectory tracking in a synchronous generator. Exploiting the flatness of the system we obtain a trajectory tracking error linearizing feedback controller which depends on the available output and its time derivatives. Using a variant of a recently introduced signal time derivative estimation approach based on the algebraic derivative method, we demonstrate, through computer simulations the effectiveness of our method even in the presence of computer generated stochastic perturbations affecting the dynamics of the system and the available measurements.

Robust stop-and-go control strategy: an algebraic approach for non-linear estimation and control

This paper describes a robust stop-and-go control strategy for vehicles. Since sensors used in a real automotive context are generally low cost, measurements are quite noisy. Furthermore, many vehicle/road interaction factors (road slope, rolling resistance, aerodynamic forces) are very poorly known. Hence, a robust strategy to noise and parameters is proposed within the same theoretical framework: algebraic non-linear estimation and control techniques. On the one hand, noisy signals will be processed to obtain accurate derivatives, and thereafter, variable estimates. On the other hand, a grey-box closed-loop control will be implemented to reject all kinds of disturbances caused by exogenous parameter uncertainties.

Algebraic change-point detection

Elementary techniques from operational calculus, differential algebra, and noncommutative algebra lead to a new approach for change-point detection, which is an important field of investigation in various areas of applied sciences and engineering. Several successful numerical experiments are presented.

CONTROL OF AN UNCERTAIN THREE-TANK SYSTEM VIA ON-LINE PARAMETER IDENTIFICATION AND FAULT DETECTION

Abstract We provide fast and on-line methods for failure detection and isolation of uncertain nonlinear systems which are operating in closed-loop. They are based on accurate values of the derivatives of a time-signal, which are obtained via new algebraic estimation techniques. The applicability and efficiency of our approach are illustrated by numerical simulations for a most popular case-study namely the three-tank system.