A Generalization of Synergistic Hybrid Feedback Control with Application to Maneuvering Control of Ships

This paper generalizes results on synergistic hybrid feedback control. Specifically, we propose a generalized definition of synergistic Lyapunov functions and feedbacks which allows the logic variable in traditional synergistic control, denoted the synergy variable, to be vector-valued and change during flows. Moreover, we introduce synergy gaps relative to components of product sets, which enables us to define jump conditions in the form of synergy gaps for different components of the synergy variable. In particular, this enables us to formulate existing hybrid output feedback control schemes within the synergistic control framework. Furthermore, we show that our generalized definition is amenable to backstepping. Finally, we give an example of how traditional synergistic control can be combined with ship maneuvering control with discrete path dynamics.