Optimal Tracking for Periodic Linear Hybrid Systems

This article provides a comprehensive characterization of the quadratic optimal tracking problem for hybrid systems with linear dynamics undergoing periodic time-driven jumps. Solutions to such a problem are proposed for both the finite horizon and the periodic cases. Furthermore, it is shown that if the reference signals are not known in advance, then the best control strategy to deal with the worst case reference signals is to simply minimize the (scaled) outputs. Finally, the derived optimal solutions are used to solve two relevant control problems, which are the reconstruction of vector fields from noisy measurements of the corresponding flows and the estimation of the time derivatives of a periodic, sampled, and noisy signal.