Distributed Discrete-time Dynamic Outer Approximation of the Intersection of Ellipsoids
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912230102007808 |
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| author | Sebastián, Eduardo Aldana-López, Rodrigo Aragüés, Rosario Montijano, Eduardo Sagüés, Carlos |
| author_facet | Sebastián, Eduardo Aldana-López, Rodrigo Aragüés, Rosario Montijano, Eduardo Sagüés, Carlos |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_01478 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Distributed Discrete-time Dynamic Outer Approximation of the Intersection of Ellipsoids Sebastián, Eduardo Aldana-López, Rodrigo Aragüés, Rosario Montijano, Eduardo Sagüés, Carlos Optimization and Control Systems and Control 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. |
| title | Distributed Discrete-time Dynamic Outer Approximation of the Intersection of Ellipsoids |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2403.01478 |