Search

In this technical note, we present a sufficient condition that guarantees identifiability for a class of linear network dynamic systems exhibiting continuous-time weighted consensus protocols. Each edge of the underlying network graph \cal G of the system is defined by a constant parameter, referred to as the weight of the edge, while each node is defined by a scalar state whose dynamics evolve as the weighted linear combination of its difference with the states of its neighboring nodes. Following the classical definition of output distinguishability, we first derive a condition that ensures the identifiability of the edge-weights of \cal G in terms of the associate transfer function. Using this characterization, we propose a sensor placement algorithm that guarantees identifiability of the edge-weights. We describe our results using illustrative examples. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the problem of localizing disturbance inputs in first-order linear time-invariant (LTI) consensus networks using measurement-based graph-theoretic methods. We consider every node and edge of the network graph to be characterized with physical weights, and show that the resulting system dynamics can be represented in terms of an asymmetric Laplacian matrix Lm. Assuming the network graph to be divided into $p$ coherent clusters, we next propose an input localization algorithm based on the properties of the weak nodal domains corresponding to the first $p-1$ slow eigenvalues of Lm. The algorithm takes in sensor measurements of the states from selected nodes, runs a system identification routine to construct the input-output transfer matrix, and compares the signs of the residues of the component transfer functions to a nominal localization key to determine in which cluster(s)the disturbance input may have entered. We prove that for systems defined over a specific class of graphs, referred to as $p$-area complete graphs, the localization is unique. We also state the extension of this result for second-order synchronization networks. We illustrate the algorithms by applying them to large-scale power system networks. [ABSTRACT FROM PUBLISHER]