Kurt Schlacher, Markus Schöberl,
"A Jet Space Approach to Check Pfaffian Systems for Flatness"
: 52nd IEEE Conference on Decision and Control, Seite(n) 2576-2581, 2013
Original Titel:
A Jet Space Approach to Check Pfaffian Systems for Flatness
Sprache des Titels:
Englisch
Original Buchtitel:
52nd IEEE Conference on Decision and Control
Original Kurzfassung:
This contribution uses the representation of control
systems, given by a set of ODEs, as Pfaffian systems. It is shown, that flatness for this class of systems is equivalent to the fact, that the unique decomposition of the pull back of the Pfaffian system to a certain jet space into a horizontal and vertical part, has a trivial horizontal part only. We present
an algorithm to construct the required jet space, as well as
the decomposition. It uses the fact, that a flat Pfaffian system
must admit a certain affine input representation after a possible
extension by contact forms. Since this representation is not unique, a branching point may appear and all branches have to be checked. This applies also to the decomposition of the system in AI representation into a horizontal and a vertical part. It is shown, how the number of branches can be reduced significantly. The algorithm requires the solution of non linear algebraic equations and the determination of flows generated
by distributions. It is worth mentioning, that the presented
approach degenerates to the well known one for input to state
linearizable system by static feedback. Finally, the application
of the algorithm to three examples, all are not input to state
linearizable by static feedback, is shown.