Tracking a periodic reference using nonlinear model predictive control

Control systems are required in diverse fields to track or reject periodic reference signals. When the reference signal is generated by a finite dimensional exosystem an interesting and important solution of the associated control design problem has been provided by Francis, Byrnes and Isidori; to implement this procedure in the nonlinear case requires solution of the Francis-Byrnes-Isidori partial differential equations that define a control invariant manifold in which the tracking error is zero and a control law that maintains the state in this manifold. This note shows how model predictive control may be employed to solve the global constrained tracking problem and thereby avoid the difficult task of determining the control invariant manifold and its associated control law. The proposed approach is illustrated by the problem of landing a vertical take-off and landing (VTOL) aircraft on an oscillating platform.