On calculating flat outputs for Pfaffian systems by a reduction procedure - Demonstrated by means of the VTOL example

This paper addresses the problem of generating a flat system parametrization for Pfaffian systems in a constructive manner. The main idea behind the procedure is a subsequent application of transformations that decompose a given Pfaffian system into a sequence of systems. This splitting of a Pfaffian system possesses the property that a parametrization of the bottom part can be elementarily obtained provided a rank criterion is met and the parametrization for the upper part is known. Then (if possible) this procedure will be repeated with the upper system to generate a sequence of systems by gradual reduction of the complexity of the problem. The application of the whole machinery to the VTOL example will demonstrate the effectiveness of the procedure. In fact the well known flat output for the VTOL and an alternative one are derived using this constructive machinery in a systematic fashion.