A Jet Space Approach to Derive Flat Outputs

This contribution uses the representation of control systems, given by a set of ODEs, as distributions on certain jet manifolds. It is shown, there exists a sequence of systems of decreasing size, such that the system is flat, if the last system is trivial, and is not flat otherwise. Although the size decreases, these systems are defined on higher order jet spaces. We present an algorithm to construct the elements of the sequence, as well as the suitable jet spaces. Their construction uses a certain property of flat systems, which allows us to construct a simpler system. In addition normalized representations are used, to keep the mathematical complexity as small as possible. It is worth mentioning, that the presented approach degenerates to the well known one for input to state linearizable systems by static feedback. Finally, the application of the algorithm to three examples, all are not input to state linearizable by static feedback, is shown.