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Abstract
We introduce the concept of an affine flat input to a non-linear system with a given output function. This approach can be seen as dual to the search for a flat output of a control system with given input. Our results provide a necessary and sufficient condition for the existence of a flat input in the SISO case, which also allows to construct of the vector field associated to the flat input. In addition, a relation between the flat input vector field and non-linear observer design is discussed. A population model is used to illustrate the construction of a flat input.
Acknowledgement
The authors dedicate the paper to Michel Fliess on the occasion of his 60th birthday. Thereby it is also acknowledged that the ideas and work of Michel Fliess have initiated many exciting research and PhD projects at Universität Stuttgart. Moreover, we thank Peter Wieland for helpful comments on a previous version of the manuscript.