Hybrid internal models for robust spline tracking

In this paper we consider the problem of tracking reference signals modeled by splines on the output of an uncertain linear system. The problem is cast in the hybrid output regulation setting. We show that any spline-based signal can be generated as the output of a linear hybrid exosystem that experiences jumps regularly over time. Then, we design a hybrid internal model-based regulator able to guarantee asymptotic tracking robustly with respect to parametric uncertainties in the plant. We show how the hybrid stabilization task implicitly present in the problem of output regulation hides interesting problems due to the fact that the hybrid exosystem generating the spline is neither continuous-time observable during flows nor discrete-time observable during jumps. Simulation results are provided in order to show the effectiveness of the design procedure.