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

• 成果类型: Article
• 署名作者: Sebastian, Eduardo; Aldana-Lopez, Rodrigo; Aragues, Rosario; Montijano, Eduardo; Sagues, Carlos
• 署名单位: University of Zaragoza; University of Zaragoza
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3540423
• 发表日期: 2025
• 页码: 4809-4816
• 关键词: Ellipsoids; optimization; Heuristic algorithms; linear programming; Approximation algorithms; Kalman filters; estimation; Symmetric matrices; Covariance matrices; Robustness; consensus; discrete time systems; distributed optimization; ellipsoidal methods

摘要

This article 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 semidefinite outer Lowner-John program, characterized by a nonseparable 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.