In this paper, we consider a network of processors aiming at cooperatively solving a convex feasibility problem in which the constraint set is the intersection of local uncertain sets, each one known only by one processor. We propose a randomized, distributed method-using concepts borrowed from a centralized ellipsoid algorithm-having finite-time convergence and working under asynchronous, time-varying and directed communication topologies. At every communication round, each processor maintains a 'candidate' ellipsoid for the global problem and performs two tasks. First, it verifies-in a probabilistic sense-if the center of the candidate ellipsoid is robustly feasible for its local set and, if not, constructs a new ellipsoid with smaller volume. Second, it exchanges its ellipsoid with neighbors, and then selects the one with smallest volume among the collected ones. We show that in a finite number of communication rounds, the processors reach consensus on a common ellipsoid whose center is-with high confidence-feasible for the entire set of uncertainty except a subset having an arbitrary small probability measure. We corroborate the theoretical results with numerical computations in which the algorithm is tested on a multi-core platform of processors communicating asynchronously.

A randomized distributed ellipsoid algorithm for uncertain feasibility problems / Chamanbaz, Mohammadreza; Notarstefano, Giuseppe; Bouffanais, Roland. - ELETTRONICO. - 2018-:(2017), pp. 1305-1310. (Intervento presentato al convegno 56th IEEE Annual Conference on Decision and Control, CDC 2017 tenutosi a Melbourne, VIC, Australia nel 12-15 Dec. 2017) [10.1109/CDC.2017.8263835].

A randomized distributed ellipsoid algorithm for uncertain feasibility problems

Notarstefano, Giuseppe;
2017

Abstract

In this paper, we consider a network of processors aiming at cooperatively solving a convex feasibility problem in which the constraint set is the intersection of local uncertain sets, each one known only by one processor. We propose a randomized, distributed method-using concepts borrowed from a centralized ellipsoid algorithm-having finite-time convergence and working under asynchronous, time-varying and directed communication topologies. At every communication round, each processor maintains a 'candidate' ellipsoid for the global problem and performs two tasks. First, it verifies-in a probabilistic sense-if the center of the candidate ellipsoid is robustly feasible for its local set and, if not, constructs a new ellipsoid with smaller volume. Second, it exchanges its ellipsoid with neighbors, and then selects the one with smallest volume among the collected ones. We show that in a finite number of communication rounds, the processors reach consensus on a common ellipsoid whose center is-with high confidence-feasible for the entire set of uncertainty except a subset having an arbitrary small probability measure. We corroborate the theoretical results with numerical computations in which the algorithm is tested on a multi-core platform of processors communicating asynchronously.
2017
2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
1305
1310
A randomized distributed ellipsoid algorithm for uncertain feasibility problems / Chamanbaz, Mohammadreza; Notarstefano, Giuseppe; Bouffanais, Roland. - ELETTRONICO. - 2018-:(2017), pp. 1305-1310. (Intervento presentato al convegno 56th IEEE Annual Conference on Decision and Control, CDC 2017 tenutosi a Melbourne, VIC, Australia nel 12-15 Dec. 2017) [10.1109/CDC.2017.8263835].
Chamanbaz, Mohammadreza; Notarstefano, Giuseppe; Bouffanais, Roland
File in questo prodotto:
File Dimensione Formato  
678757_disclaimer.pdf

accesso aperto

Tipo: Postprint
Licenza: Licenza per accesso libero gratuito
Dimensione 875.94 kB
Formato Adobe PDF
875.94 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/678757
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 0
social impact