A fundamental element of effective operation of autonomous systems is the need for appropriate sensing and processing of measurements to enable desired system perception and corresponding actions. Further, for distributed frameworks, the sensing structures must operate in the presence of constraints on sensor availability, dynamic group membership, noise in the measurements, and disturbances from the environment. A promising approach for constructing a viable framework for analysis of both engineered and biological multiagent systems is the intersection of geometric nonlinear systems theory and empirical Gramian methods. Given a network, we would like to determine which subset of nodes should be measured by limited sensing facilities to maximize information about the entire network. The optimal choice corresponds to the configuration that returns the highest value of a measure of observability of the system. Additionally, the effects of changes in the topology of the corresponding graph of a network on the observability of the network are investigated. We extend observability metrics based on the empirical observability Gramian from deterministic nonlinear systems to nonlinear stochastic systems in order to capture the impact of process noise on observability. We demonstrate that the empirical observability Gramian can be used to provide an equivalent condition for a definition of stochastic observability on linear systems, and that the Gramian can be used to extend stochastic observability to nonlinear stochastic systems. We further demonstrate through simulation that consideration of process noise can reveal observability in systems that would be considered unobservable using traditional deterministic tools. These ideas will be discussed relative to both engineering applications for autonomous multiagent systems, network synthesis with privacy guarantees, tracking of disease spread between networks of communities, and effective strain sensor placement on insect wings for inertial measurements.
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