Approximate tracking near singularities. A differential algebraic approach

In this work, recent results based on differential algebra tools are used for the synthesis of a dynamical feedback controller for a SISO nonlinear system exhibiting points of singularity. An approximated inversion-based controlled is synthetized using the Flies' generalized observability canonical form (GOCF) associated to the system. The basic idea is to search for an approximate system, which does not exhibits points of singularity, and for which an exact inversion-based (dynamical) controller can be calculated. This controller, when applied to the original system, guarantees bounded tracking error near the singularities, provided certain functions are bounded for small values of their arguments.<>