A priori identification of the ‘natural’ regular zero dynamics foliation for dynamic extension

Determine, for a given nonlinear control system that admits feedback linearization via an extension system, how to identify a priori the corresponding regular zero dynamics foliation whose dynamic extension leads to a feedback linearizable system, thereby eliminating the need for search.

Background

The paper shows that if a system becomes feedback linearizable after an extension, then one can realize this via a sequence of one-step dynamic extensions (LSOP class). In this context, the regular zero dynamics foliation associated with the extension system appears to be the ‘natural’ choice to guide the extension.

However, this ‘natural’ foliation is not known ahead of time for the base system, motivating the dynamic search approach proposed in the paper. The open question asks for a principled way to identify this foliation without resorting to search.