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arXiv · 2403.01478

Distributed Discrete-time Dynamic Outer Approximation of the Intersection of Ellipsoids

Eduardo Sebastián·Rodrigo Aldana-López·Rosario Aragüés·Eduardo Montijano·Carlos Sagüés
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Abstract

This paper presents the first discrete-time distributed algorithm to track the tightest ellipsoids that outer approximates the global dynamic intersection of ellipsoids. Given an undirected network, we consider a setup where each node measures an ellipsoid, defined as a time-varying positive semidefinite matrix. The goal is to devise a distributed algorithm to track the tightest outer approximation of the intersection of all the ellipsoids. The solution is based on a novel distributed reformulation of the original centralized semi-definite outer L\"owner-John program, characterized by a non-separable objective function and global constraints. We prove finite-time convergence to the global minima of the centralized problem in the static case and finite-time bounded tracking error in the dynamic case. Moreover, we prove boundedness of estimation in the tracking of the global optimum and robustness in the estimation against time-varying inputs. We illustrate the properties of the algorithm with different simulated examples, including a distributed estimation showcase where our proposal is integrated into a distributed Kalman filter to surpass the state-of-the-art in mean square error performance.

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Eduardo Sebastián, Rodrigo Aldana-López, Rosario Aragüés, Eduardo Montijano, Carlos Sagüés. 2024-03-03. Distributed Discrete-time Dynamic Outer Approximation of the Intersection of Ellipsoids. https://arxiv.org/abs/2403.01478

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