Structural Controllability of Undirected Diffusive Networks With Vector-Weighted Edges

Abstract

In this paper, controllability of undirected networked systems with diffusively coupled subsystems is considered, where each subsystem is of identically fixed general high-order singleinput-multi-output dynamics. The underlying graph of the network topology is vector-weighted. The aim is to find conditions under which the networked system is structurally controllable, i.e., for almost all vector values for interaction links of the network topology, the corresponding system is controllable. It is proven that, the networked system is structurally controllable, if and only if each subsystem is controllable and observable, and the network topology is globally input-reachable. These conditions are further extended to the cases with multi-input-multi-output subsystems and matrixweighted edges, or where both directed and undirected interaction links exist.

Structural controllability of networked systems with general heterogeneous subsystems

“…The works in [32,34] show that to an undirected diffusive network composed of identical subsystems or a network composed of SISO subsystems, the networked system is structurally controllable only if each subsystem is structurally observable. Here we mainly focus on the relations between structural controllability of the system (3) and the network topology L as well as subsystem interconnections W ij , where subsystems have heterogeneous MIMO dynamics.…”

“…Besides, considering the case that subsystem dynamics, as well as interconnections between them, are fixed while control inputs can be selected independently, the works in [28][29][30][31] study the problem of selecting minimum control inputs to ensure structural controllability of the network. When it comes to the case that to a networked system, the subsystem dynamics are fixed while the subsystem interconnections can be constructed independently, structural controllability of the network is considered in [32][33][34] through constructing subsystem interconnections as well as network topology. More specifically, the works in [32] consider structural controllability of undirected diffusive networks composed of identical single-input-multi-output (SIMO) subsystems and generalize the results to the case with identical MIMO subsystems.…”

“…When it comes to the case that to a networked system, the subsystem dynamics are fixed while the subsystem interconnections can be constructed independently, structural controllability of the network is considered in [32][33][34] through constructing subsystem interconnections as well as network topology. More specifically, the works in [32] consider structural controllability of undirected diffusive networks composed of identical single-input-multi-output (SIMO) subsystems and generalize the results to the case with identical MIMO subsystems. In [33,34], networks composed of identical/heterogeneous SISO subsystems are considered, respectively.…”

Generic Detectability and Isolability of Topology Failures in Networked Linear Systems

“…Remark 1: In literature, the assumption of knowing subsystem dynamics but with little/no knowledge on the subsystem interaction weights is common in many aspects on networked systems, including topology reconstruction [27], system identification [28], as well as structural controllability [22,23].…”

“…In control theory, some properties will become generic in this class of systems, i.e., either for almost all systems in this class, these properties hold true, or for none these properties hold true. For example, controllability and observability are two well-known generic properties, both for a lumped structured plant [21] and a networked system [22,23].…”