Sur la détermination des sorties plates par calcul formel

Dans ce papier, nous étudions la possibilité de déterminer les sorties plates d'un système non linéaire par calcul formel. Rappelons qu'une sortie plate est une sortie généralisée particulière telle que toutes les courbes intégrales du syst`eme peuvent s'exprimer comme les images, par une application infiniment dérivable, des composantes de cette sortie plate et d'un nombre fini de ses dérivées successives par rapport au temps. Nous utilisons ici les caractérisations récentes de [1], [2] dans le cadre des variétés de jets d'ordre infini (voir par ex. [3], [4]). Les étapes successives de l'algorithme formel sont discutées sur l'exemple classique du véhicule non holonome

Flatness Characterization: Two Approaches

We survey two approaches to flatness necessary and sufficient conditions and compare them on examples

Towards a Computer Algebraic Algorithm for Flat Output Determination

This contribution deals with nonlinear control systems. More precisely, we are interested in the formal computation of a so-called flat output, a particular generalized output whose property is, roughly speaking, that all the integral curves of the system may be expressed as smooth functions of the components of this flat output and their successive time derivatives up to a finite order (to be determined). Recently, a characterization of such flat output has been obtained in [14, 15], in the framework of manifolds of jets of infinite order (see e.g. [18, 9]), that yields an abstract algorithm for its computation. In this paper it is discussed how these conditions can be checked using computer algebra. All steps of the algorithm are discussed for the simple (but rich enough) example of a non holonomic car

On the computation of π-flat outputs for differential-delay systems

We introduce a new definition of π-flatness for linear differential delay systems with time-varying coefficients. We characterize π- and π-0-flat outputs and provide an algorithm to efficiently compute such outputs. We present an academic example of motion planning to discuss the pertinence of the approach