A Lie-Group Approach for Nonlinear Dynamic Systems Described by Implicit Ordinary Differential Equations

This contribution presents a Lie-group based approach for the accessibility and the observability problem of dynamic systems described by a set of implicit ordinary differential equations. It is shown that non-accessible or non-observable systems admit Lie-groups acting on their solutions such that dinstinguished parts of the system remain unchanged. The presented methods use the fact that the dynamic sytem may be identified with a submanifold in a suitable jet-bundle. Therefore, a short introduction to this theory,as well as its application to systems of differential equations is presented.