Identifiability of dynamical networks: Which nodes need be measured?

Abstract

Much recent research has dealt with the identifiability of a dynamical network in which the node signals are connected by causal linear time-invariant transfer functions and are possibly excited by known external excitation signals and/or unknown noise signals. So far all results on the identifiability of the whole network have assumed that all node signals are measured. Under this assumption, it has been shown that such networks are identifiable only if some prior knowledge is available about the structure of the network, in particular the structure of the excitation. In this paper we present the first results for the situation where not all node signals are measurable, under the assumptions that the topology of the network is known, that each node is excited by a known signal and that the nodes are noise-free. Using graph theoretical properties, we show that the transfer functions that can be identified depend essentially on the topology of the paths linking the corresponding vertices to the measured nodes. An important outcome of our research is that, under those assumptions, a network can often be identified using only a small subset of node measurements.

Allocation of Excitation Signals for Generic Identifiability of Dynamic Networks

“…Following [27], [30], a path-based condition for the generic identifiability ofΣ is that the maximum number of mutually vertex-disjoint paths from P + j to C is equal to |P + j | for all i ∈ V (Ǧ), where P + j is a subset of the out-neighbors of j: P + j := {i ∈ N + j | G ij (θ) is parameterized}. Thereby, we define the concept of anti-pseudotrees.…”

Identifiability of Undirected Dynamical Networks: A Graph-Theoretic Approach

“…The papers that are most closely related to the work in this paper are [17] and [18]. Nabavi et al [17] consider weighted, undirected consensus networks with a single input.…”

“…Note that the above papers make explicit assumptions on the number of input or output nodes. Indeed, in [17] there is a single input node, all nodes are input nodes in [18], and all nodes are measured in [20]. In contrast to these papers, the current paper considers graph-theoretic conditions for identifiability of dynamical networks where the sets of input and output nodes can be any two (known) subsets of the vertex set.…”

Necessary and Sufficient Topological Conditions for Identifiability of Dynamical Networks

“…Therefore, the question is which transfer functions in G(z) can be uniquely reconstructed from the transfer matrix CT (z; G). In recent work [4], [24] this question has been considered for generic identifiability. Graph-theoretic conditions were given under which a set of transfer functions can be uniquely identified from CT (z; G) for almost all network matrices G consistent with the graph.…”