Trackability filtering for underactuated systems

Underactuated systems are commonplace and present a challenge in designing tracking controllers. Foremost among these are vehicles, like passenger cars and aircraft. Such systems with more outputs than control inputs are not right invertible. As a result continuous control laws cannot, in general, be designed to track arbitrary reference signals. We present a Trackable Filter design which produces an augmented reference signal as close as possible to the original reference which the underactuated system can track with zero error. The resulting control law can be either discontinuous or continuous by the choice of the designer.