Computer-Algebra Algorithms for the Geometric Controller Design of DAEs

This contribution discusses an approach to extend geometric controller design techniques known for systems of implicit ordinary differential equations to computer algebra algorithms for systems of implicit ordinary differential equations also known as DAEs (differential algebraic equations), a system class which arises in some modeling approaches for, e.g., electrical or mechanical systems. Shortly, the methodology used to derive published algorithms on, e.g., observability of implicit systems is reviewed. This geometric approach is based on the formally integrable form of the implicit system. Using this idea it is shown in this contribution how the static feedback linearization of dynamical systems can be adapted to be carried out directly at the formally integrable implicit system without having to deal with the explicit form. The approach is shown with the help of mechanical example - the Car&Beam system.