4,727 research outputs found

    The Observability Radius of Networks

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    This paper studies the observability radius of network systems, which measures the robustness of a network to perturbations of the edges. We consider linear networks, where the dynamics are described by a weighted adjacency matrix, and dedicated sensors are positioned at a subset of nodes. We allow for perturbations of certain edge weights, with the objective of preventing observability of some modes of the network dynamics. To comply with the network setting, our work considers perturbations with a desired sparsity structure, thus extending the classic literature on the observability radius of linear systems. The paper proposes two sets of results. First, we propose an optimization framework to determine a perturbation with smallest Frobenius norm that renders a desired mode unobservable from the existing sensor nodes. Second, we study the expected observability radius of networks with given structure and random edge weights. We provide fundamental robustness bounds dependent on the connectivity properties of the network and we analytically characterize optimal perturbations of line and star networks, showing that line networks are inherently more robust than star networks.Comment: 8 pages, 3 figure

    The Observability Radius of Networks

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    This paper studies the observability radius of network systems, which measures the robustness of a network to perturbations of the edges. We consider linear networks, where the dynamics are described by a weighted adjacency matrix and dedicated sensors are positioned at a subset of nodes. We allow for perturbations of certain edge weights with the objective of preventing observability of some modes of the network dynamics. To comply with the network setting, our work considers perturbations with a desired sparsity structure, thus extending the classic literature on the observability radius of linear systems. The paper proposes two sets of results. First, we propose an optimization framework to determine a perturbation with smallest Frobenius norm that renders a desired mode unobservable from the existing sensor nodes. Second, we study the expected observability radius of networks with given structure and random edge weights. We provide fundamental robustness bounds dependent on the connectivity properties of the network and we analytically characterize optimal perturbations of line and star networks, showing that line networks are inherently more robust than star networks

    The Formation of Networks with Local Spillovers and Limited Observability

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    In this paper I analyze the formation of networks in which each agent is assumed to possess some information of value to the other agents in the network. Agents derive payoff from having access to the information of others through communication or spillovers through the links between them. Linking decisions are based on network-dependent marginal payoff and a network independent noise capturing exogenous idiosyncratic effects. Moreover, agents have a limited observation radius when deciding to whom to form a link. I find that for small noise the observation radius does not matter and strongly centralized networks emerge. However, for large noise, a smaller observation radius generates networks with a larger degree variance. These networks can also be shown to have larger aggregate payoff. I then estimate the model using a network of coinventors, firm alliances and trade relationships between countries, and find that the model can closely reproduce the observed patterns. The estimates show that with increasing levels of aggregation, the observation radius is increasing, indicating economies of scale in which larger organizations are able to process greater amounts of information.diffusion, network formation, growing networks, limited observability

    Space-Time Sampling for Network Observability

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    Designing sparse sampling strategies is one of the important components in having resilient estimation and control in networked systems as they make network design problems more cost-effective due to their reduced sampling requirements and less fragile to where and when samples are collected. It is shown that under what conditions taking coarse samples from a network will contain the same amount of information as a more finer set of samples. Our goal is to estimate initial condition of linear time-invariant networks using a set of noisy measurements. The observability condition is reformulated as the frame condition, where one can easily trace location and time stamps of each sample. We compare estimation quality of various sampling strategies using estimation measures, which depend on spectrum of the corresponding frame operators. Using properties of the minimal polynomial of the state matrix, deterministic and randomized methods are suggested to construct observability frames. Intrinsic tradeoffs assert that collecting samples from fewer subsystems dictates taking more samples (in average) per subsystem. Three scalable algorithms are developed to generate sparse space-time sampling strategies with explicit error bounds.Comment: Submitted to IEEE TAC (Revised Version

    Time-triggering versus event-triggering control over communication channels

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    Time-triggered and event-triggered control strategies for stabilization of an unstable plant over a rate-limited communication channel subject to unknown, bounded delay are studied and compared. Event triggering carries implicit information, revealing the state of the plant. However, the delay in the communication channel causes information loss, as it makes the state information out of date. There is a critical delay value, when the loss of information due to the communication delay perfectly compensates the implicit information carried by the triggering events. This occurs when the maximum delay equals the inverse of the entropy rate of the plant. In this context, extensions of our previous results for event triggering strategies are presented for vector systems and are compared with the data-rate theorem for time-triggered control, that is extended here to a setting with unknown delay.Comment: To appear in the 56th IEEE Conference on Decision and Control (CDC), Melbourne, Australia. arXiv admin note: text overlap with arXiv:1609.0959

    Calibration by correlation using metric embedding from non-metric similarities

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    This paper presents a new intrinsic calibration method that allows us to calibrate a generic single-view point camera just by waving it around. From the video sequence obtained while the camera undergoes random motion, we compute the pairwise time correlation of the luminance signal for a subset of the pixels. We show that, if the camera undergoes a random uniform motion, then the pairwise correlation of any pixels pair is a function of the distance between the pixel directions on the visual sphere. This leads to formalizing calibration as a problem of metric embedding from non-metric measurements: we want to find the disposition of pixels on the visual sphere from similarities that are an unknown function of the distances. This problem is a generalization of multidimensional scaling (MDS) that has so far resisted a comprehensive observability analysis (can we reconstruct a metrically accurate embedding?) and a solid generic solution (how to do so?). We show that the observability depends both on the local geometric properties (curvature) as well as on the global topological properties (connectedness) of the target manifold. We show that, in contrast to the Euclidean case, on the sphere we can recover the scale of the points distribution, therefore obtaining a metrically accurate solution from non-metric measurements. We describe an algorithm that is robust across manifolds and can recover a metrically accurate solution when the metric information is observable. We demonstrate the performance of the algorithm for several cameras (pin-hole, fish-eye, omnidirectional), and we obtain results comparable to calibration using classical methods. Additional synthetic benchmarks show that the algorithm performs as theoretically predicted for all corner cases of the observability analysis

    Model Reduction for Complex Hyperbolic Networks

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    We recently introduced the joint gramian for combined state and parameter reduction [C. Himpe and M. Ohlberger. Cross-Gramian Based Combined State and Parameter Reduction for Large-Scale Control Systems. arXiv:1302.0634, 2013], which is applied in this work to reduce a parametrized linear time-varying control system modeling a hyperbolic network. The reduction encompasses the dimension of nodes and parameters of the underlying control system. Networks with a hyperbolic structure have many applications as models for large-scale systems. A prominent example is the brain, for which a network structure of the various regions is often assumed to model propagation of information. Networks with many nodes, and parametrized, uncertain or even unknown connectivity require many and individually computationally costly simulations. The presented model order reduction enables vast simulations of surrogate networks exhibiting almost the same dynamics with a small error compared to full order model.Comment: preprin
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