Structural Target Controllability of Undirected Networks

Abstract

In this paper, we study the target controllability problem of networked dynamical systems, in which we are tasked to steer a subset of network states towards a desired objective. More specifically, we derive necessary and sufficient conditions for the structural target controllability problem of linear time-invariant (LTI) systems with symmetric state matrices, such as undirected dynamical networks with unknown link weights. To achieve our goal, we first characterize the generic rank of symmetrically structured matrices, as well as the modes of any numerical realization. Subsequently, we provide a graph-theoretic necessary and sufficient condition for the structural controllability of undirected networks with multiple control nodes, for which there are no previous results in the literature. Finally, we derive a graph-theoretic necessary and sufficient condition for structural target controllability of undirected networks. Remarkably, apart from the standard reachability condition, only local topological information is needed for the verification of structural target controllability. arXiv:1809.06773v2 [math.OC]

Structural Controllability of Undirected Diffusive Networks With Vector-Weighted Edges

“…Such setting is obviously different from the class of systems studied in this paper. It is also mentionable that (strong) structural controllability of networks of single-integrators with symmetric weights (or more complicated dependencies than symmetry) has recently received much attention in [17][18][19][20]. This paper differs from these works in the sense that dependencies exist between self-loop of a vertex and the edges connecting to it.…”

Target controllability of multiagent systems under fixed and switching topologies

“…Instead, it is more feasible and sufficient to achieve target control of MASs, that is, to control a subset of agents. This specific form of output controllability is known under the name target controllability . In the recent literature, the target controllability has been intensively studied by many researchers.…”

“…To the best of our knowledge, however, the existing results considered target controllability under structural (strongly structurally) controllability framework. Thus, the results inevitably ignored the effects of link weights on target controllability . On the other hand, the existing results of target controllability are only pertinent to the fixed interaction topology while switching topology is left largely unconsidered …”

“…[34][35][36][37][38] In the recent literature, the target controllability has been intensively studied by many researchers. Examples include the target controllability of complex networks, 34,35 strong target controllability of dynamical networks, 36,37 structural target controllability of undirected networks, 38 and target controllability of biomolecular networks. 39 To the best of our knowledge, however, the existing results considered target controllability under structural (strongly structurally) controllability framework.…”

“…34,35,[37][38][39] On the other hand, the existing results of target controllability are only pertinent to the fixed interaction topology while switching topology is left largely unconsidered. [34][35][36][37][38][39] In this paper, we study the target controllability of MASs under fixed and switching topologies. For fixed interaction topology, we provide some necessary and/or sufficient algebraic and graph-theoretic conditions for target controllability and analyze the effects of the directed and weighted interaction topology on target controllability.…”