# Towards a Computer Algebraic Algorithm for Flat Output Determination

**Authors**: Felix Antritter, Jean Lévine, International Symposium on Symbolic and Algebraic Computation, July 20 2008, Hagenberg, Austria

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.

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**BibTeX**:

@Proceedings{,

author = {Felix Antritter, Jean Lévine},

editor = {},

title = {Towards a Computer Algebraic Algorithm for Flat Output Determination},

booktitle = {International Symposium on Symbolic and Algebraic Computation},

volume = {},

publisher = {},

address = {Hagenberg},

pages = {},

year = {2008},

abstract = {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.},

keywords = {}}