Linear time-varying tracking control with application to Unmanned Aerial Vehicles

This paper presents a novel control algorithm for tracking of nonlinear dynamic systems. The tracking problem leads to linearized time-varying error equations. Hence new eigenvalue notions are introduced for linear time varying systems, and a PD eigenstructure assignment scheme is proposed for linear time-varying structure via a differential Sylvester equation. Also shown is that closed-loop systems could be stabilized by assigning PD-eigenvalues appropriately, and a desired performance could be obtained by assigning the PD-eigenvectors according to the design specifications. The present control algorithm has an internal framework for testing the controllability of the time varying system via Lyapunov transform. The algorithm proposed is very general, and in principle applicable to systems of any order of complexity with any degree or kind of nonlinearity. An Unmanned Aerial Vehicle flight control application for a real aircraft is presented to validate the proposed algorithm.