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

Sebastián, Eduardo (Universidad de Zaragoza) ; Aldana-López, Rodrigo ; Aragüés, Rosario (Universidad de Zaragoza) ; Montijano, Eduardo (Universidad de Zaragoza) ; Sagüés, Carlos (Universidad de Zaragoza)

Resumen: 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 Löwner-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.

Idioma: Inglés

DOI: 10.1109/TAC.2025.3540423

Año: 2025

Publicado en: IEEE TRANSACTIONS ON AUTOMATIC CONTROL (2025), [8 pp.]
ISSN: 0018-9286

Tipo y forma: Article (Published version)

Área (Departamento): Área Ingen.Sistemas y Automát. (Dpto. Informát.Ingenie.Sistms.)