# Multi-Scale Analysis of Multi-Agent Coverage Control Algorithms

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Description:

As the sizes of networked systems and swarms increase dramatically, new challenges arise from algorithm performance evaluation and design, and agent-level algorithm implementation. This calls for a consistent, multi-scale approach that can bridge the gap between small and large agent-set cases. With this in mind, this talk presents a new class of proximal descent schemes for the transport of probability measures in the  $L^2$-Wasserstein space. These algorithms are then projected onto the underlying Euclidean space to obtain the corresponding descent scheme for individual agents. In particular, we establish a  relationship to previous coverage control schemes based on Voronoi partitions and obtain the following insights: (i) our results establish that in the $N$ infinity limit, previously considered gradient descent-based transport schemes achieve convergence to global minimizers of typical aggregate objective functions ---even if the convergence is only local for any finite $N$, and (ii) the most basic distortion performance metric of coverage control does not result in the desired performance in the $N$ infinity limit.

Speaker:
Sonia Martinez Diaz, UC San Diego Jacobs School of Engineering
Location:
Virtual
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