The control of dynamical processes in networks is considered, in the case where measurement and actuation capabilities are sparse and possibly remote. Specifically, we study control of a canonical network dynamics, when only one network component's state can be measured and only one (in general different) component can be actuated. To do so, we characterize the finite-and infinite-zeros of the resulting SISO system in terms of the graph topology. Using these results, we establish graph-theoretic conditions under which there are zeros in the closed right-half plane. These conditions depend on the length, strength, and number of the paths from the component where the input is applied to the component where the measurements are made. Then, we present the implications of these conditions on the controller design task focusing in stabilizations/destabilization of network processes under static negative feedback.
h i g h l i g h t s• We study detection of network changes from remote noisy time-series measurements.• A Maximum A-Posteriori Probability hypothesis testing scheme is employed.• Relationships between the network topology and MAP detector performance are developed. • Detector performance depends on presence of certain paths in the network. • Simulations demonstrate the analytical results developed.
a b s t r a c tWe study whether local structural changes in a complex network can be distinguished from passive remote time-course measurements of the network's dynamics. Specifically the detection of link failures in a network synchronization process from noisy measurements at a single network component is considered. By phrasing the detection task as a Maximum A Posteriori Probability hypothesis testing problem, we are able to obtain conditions under which the detection is (1) improved over the a priori and (2) asymptotically perfect, in terms of the network spectrum and graph. We find that, in the case where the detector has knowledge of the network's state, perfect detection is possible under general connectivity conditions regardless of the measurement location. When the detector does not have state knowledge, a remote signature permits improved but not perfect detection, under the same connectivity conditions. At its essence, detectability is achieved because of the close connection between a network's topology, its eigenvalues and local response characteristics.
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