Construction of flat outputs by reduction and elimination
Sprache des Vortragstitels:
The construction of flat outputs for nonlinear lumped parameter systems is still a challenging problem in the general case, although significant progresses have been made in the last years. An algorithm, based on successive reduction of the number of variables and elimination of variables, equivalent to a reduction of the number of equations, is presented. Since the structure of the reduced system is essential, whether further simplifications are possible, the geometric structure of undetermined systems of implicit
differential equations will be studied. It will turn out, that the dynamic extension of the system, such that it is transformable to a form affine in the derivative coordinates, is the essential tool. Locally necessary and sufficient condition for the existence of such an extension, which leads to a reduction, will be presented. The geometric interpretation is that certain vector-fields become projectable on the manifold defined by the extended system or that a certain distribution is stable with respect to a covariant derivative. In addition, the use of the derived flag of an explicit control system allows us to give a straightforward interpretation of the properties presented above. Finally some applications of this approach are presented.