# ON THE IMPLEMENTATION IN MAPLE OF NECESSARY AND SUFFICIENT CONDITIONS FOR FLATNESS

2 novembre 2009, Salle V111, à l'Ecole des Mines, Paris.

14h00 : Gregor VERHOEVEN, Universität der Bundeswehr, München.

In this talk a toolbox for the Computer-Algebra System Maple for the computation of flat outputs of nonlinear control systems is presented.

Recall that a flat output is 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. Recently, a characterization of such flat output has been obtained in the framework of manifolds of jets of infinite order, that yields an abstract algorithm for its computation.

The toolbox allows to perform all steps of the proposed abstract algorithm within one framework. The conditions of the algorithm make use of differential operators which combine differential geometric concepts like exterior derivative and wedge product as well as algebraic concepts as operations on skew polynomials with coefficients that are meromorphic functions of the coordinates. Existing computer algebra systems only offer functionalities for each of the mentioned fields separately like the DifferentialGeometry toolbox for Maple but the combination of the different concepts is not considered. The combined treatment of all the different aspects of the conditions was the main challenge of the project.

14h00 : Gregor VERHOEVEN, Universität der Bundeswehr, München.

In this talk a toolbox for the Computer-Algebra System Maple for the computation of flat outputs of nonlinear control systems is presented.

Recall that a flat output is 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. Recently, a characterization of such flat output has been obtained in the framework of manifolds of jets of infinite order, that yields an abstract algorithm for its computation.

The toolbox allows to perform all steps of the proposed abstract algorithm within one framework. The conditions of the algorithm make use of differential operators which combine differential geometric concepts like exterior derivative and wedge product as well as algebraic concepts as operations on skew polynomials with coefficients that are meromorphic functions of the coordinates. Existing computer algebra systems only offer functionalities for each of the mentioned fields separately like the DifferentialGeometry toolbox for Maple but the combination of the different concepts is not considered. The combined treatment of all the different aspects of the conditions was the main challenge of the project.