On symmetric continuum opinion dynamics

This paper investigates the asymptotic behavior of some common opinion dynamic models in a continuum of agents. We show that as long as the interactions among the agents are symmetric, the distribution of the agents' opinion converges. We also investigate whether convergence occurs in a stronger sense than merely in distribution, namely, whether the opinion of almost every agent converges. We show that while this is not the case in general, it becomes true under plausible assumptions on inter-agent interactions, namely that agents with similar opinions exert a non-negligible pull on each other, or that the interactions are entirely determined by their opinions via a smooth function.Comment: 28 pages, 2 figures, 3 file

Cooperative learning in multi-agent systems from intermittent measurements

Motivated by the problem of tracking a direction in a decentralized way, we consider the general problem of cooperative learning in multi-agent systems with time-varying connectivity and intermittent measurements. We propose a distributed learning protocol capable of learning an unknown vector $\mu$ from noisy measurements made independently by autonomous nodes. Our protocol is completely distributed and able to cope with the time-varying, unpredictable, and noisy nature of inter-agent communication, and intermittent noisy measurements of $\mu$. Our main result bounds the learning speed of our protocol in terms of the size and combinatorial features of the (time-varying) networks connecting the nodes

Optimal Topology Design for Disturbance Minimization in Power Grids

The transient response of power grids to external disturbances influences their stable operation. This paper studies the effect of topology in linear time-invariant dynamics of different power grids. For a variety of objective functions, a unified framework based on $H_2$ norm is presented to analyze the robustness to ambient fluctuations. Such objectives include loss reduction, weighted consensus of phase angle deviations, oscillations in nodal frequency, and other graphical metrics. The framework is then used to study the problem of optimal topology design for robust control goals of different grids. For radial grids, the problem is shown as equivalent to the hard "optimum communication spanning tree" problem in graph theory and a combinatorial topology construction is presented with bounded approximation gap. Extended to loopy (meshed) grids, a greedy topology design algorithm is discussed. The performance of the topology design algorithms under multiple control objectives are presented on both loopy and radial test grids. Overall, this paper analyzes topology design algorithms on a broad class of control problems in power grid by exploring their combinatorial and graphical properties.Comment: 6 pages, 3 figures, a version of this work will appear in ACC 201