Structural Controllability of an NDS With LFT Parameterized Subsystems

Abstract

This paper studies structural controllability for a networked dynamic system (NDS), in which each subsystem may have different dynamics, and unknown parameters may exist both in subsystem dynamics and in subsystem interconnections. In addition, subsystem parameters are parameterized by a linear fractional transformation (LFT). It is proven that controllability keeps to be a generic property for this kind of NDSs. Some necessary and sufficient conditions are then established respectively for them to be structurally controllable, to have a fixed uncontrollable mode, and to have a parameter dependent uncontrollable mode, under the condition that each subsystem interconnection link can take a weight independently. These conditions are scalable, and in their verifications, all arithmetic calculations are performed separately on each subsystem. In addition, these conditions also reveal influences on NDS controllability from subsystem input-output relations, subsystem uncontrollable modes and subsystem interconnection topology. Based on these observations, the problem of selecting the minimal number of subsystem interconnection links is studied under the requirement of constructing a structurally controllable NDS. A heuristic method is derived with some provable approximation bounds and a low computational complexity.

Structural Controllability of Undirected Diffusive Networks With Vector-Weighted Edges

“…Lemma 1 ( [22], [12]): The pair (A, B) in (7) is structurally controllable, if and only if 1) Every cycle is input-…”

“…is a vector-weighted Laplacian [14]. Throughout this paper, without losing of generality, assume that c k = 0, for k = 1, ..., r. The (1)-(2) models a diffusive networked system with identical subsystems, which arises in modeling interacted liquid tanks [4], synchronizing networks of linear oscillators [1,12], electrical networks [15], consensus-based MASs [3], etc. Specially, when r = 1, (1)-(2) becomes a networked system with SISO subsystems.…”

“…On the other hand, controllability of networked systems with high-order subsystems has also attracted much research interests in [8][9][10][11][12][13]. To be specific, [8,11,13] focused on networked systems with identical subsystems (called homogeneous networks), whiles [9,10,12] on networked systems with general heterogeneous subsystems (called heterogeneous networks). Particularly, controllability as a generic property for a networked system is studied in [12,13].…”

“…However, except [9,10,12] which focus on heterogeneous networks, almost all results on controllability of homogeneous networks are built on the condition that all weights of edges in the network topology belong to {0, 1} or some scalars [2, 5-8, 11, 13]. Notice that, when each subsystem is not of single-input-single-output (SISO), there is a typical situation that different interaction channels between two subsystems are weighted differently, either because of differences in the nature of physical variables they convey, or the variants of the channels themselves.…”

Sparsest Input Selection for Controllability of Singular Systems via a Two-Step Greedy Algorithm

“…Related Work: Controllability and observability of largescale networked dynamical systems have drawn the attention of control scientists [12]- [14]. As mentioned earlier, determining the minimal number of actuated states to ensure controllability for nonsingular systems has been proven to be NP-hard [2].…”