Characterizing Network Controllability and Observability for Abstractions and Realizations of Dynamic Networks
Charles A. Johnson, Sean C. Warnick · IFAC-PapersOnLine · 2020
One method for managing the complexity of a dynamic network is to abstract some of this complexity away by using a simpler, yet behaviorally equivalent, mathematical model. A theory for such abstractions is currently under development (cf. Kivits and Van den Hof (2018) as well as Woodbury and Warnick (2019)). While recent work has considered concepts of controllability and observability for networked dynamic systems (cf. Xiang et al. (2019) and Liu and Barabási (2016)), this paper analyzes these concepts for abstractions of dynamic networks. In particular, we present the notion of a complete abstraction and an extraneous realization of a dynamic network and show that these concepts characterize the controllability and observability properties of a class of abstractions of dynamic networks.