A Framework for Inference and Identification of Hybrid-System Models: Mixed Event-Time-driven Systems (METS)

This paper proposes a simplified framework for the experimental inference and identification of models of hybrid systems. A problematic feature of such system identification is the presence of different ``modes'' of evolution of continuous state variables: this may necessitate not only the identification of the dynamics of the different modes, but also the identification of changes of mode. Inspired by the idea that the physics underlying the system is often invariant, this paper proposes a simplified framework that models hybrid systems in the form of separate untimed, ``event-driven'' and dynamical, ``time-driven'' components that are coupled only through input and output signals. Signals from the event-driven component are assumed to affect the dynamics of the time-driven component only in a relatively limited manner -- either as direct inputs, or by modulating output feedback within the time-driven component; the ``intrinsic,'' ``open-loop'' dynamics of the time-driven component do not change. These assumptions largely decouple the estimation of the event- and time-driven components, avoiding the problem of distinguishing separate modes, and permitting the leveraging of standard system-identification methods. Two well known examples serve to illustrate the approach.