On the formal characterization of reduced-order flat outputs over an ore algebra

In this paper, a formal and effective methodology is proposed to characterize a subset of reduced-order flat outputs for nonlinear implicit systems described in the differential geometric framework of jets of infinite order. The proposed methodology includes an original management of the degrees of freedom left by the polynomial matrices approach. First, a reduced-order basis of the free left D-module, finitely presented by the variational system, is obtained by computing some reduced-order bases of the left nullspace of Ore polynomial matrices and by using the weak Popov form over an Ore algebra. Under the assumption that the latter module is free, a structural constraint is introduced in the generalized Cartan moving frame structure equations in order to obtain a subset of reduced-order flat outputs.