EXTENDING ROBUSTNESS AND RANDOMIZATION FROM CONSENSUS TO SYMMETRIZATION ALGORITHMS

作     者：Mazzarella, Luca Ticozzi, Francesco Sarlette, Alain 

作者机构：Univ Padua Dipartimento Ingn Informaz I-35131 Padua Italy Dartmouth Coll Dept Phys & Astron Hanover NH 03755 USA PSL Res Univ QUANTIC Project Team INRIA Paris Rocquencourt Paris France Univ Ghent SYSTeMS B-9052 Ghent Belgium 

出 版 物：《SIAM JOURNAL ON CONTROL AND OPTIMIZATION》 (工业与应用数学会控制与最佳化杂志)

年 卷 期：2015年第53卷第4期

页      面：2076-2099页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0811[工学-控制科学与工程] 0701[理学-数学] 

主　　题：symmetry groups robust algorithms distributed algorithms consensus random state generation 

摘      要：This work interprets and generalizes consensus-type algorithms as switching dynamics leading to symmetrization of some vector variables with respect to the actions of a finite group. We show how the symmetrization framework we develop covers applications as diverse as consensus on probability distributions (either classical or quantum), uniform random state generation, and open-loop disturbance rejection by quantum dynamical decoupling. Robust convergence results are explicitly provided in a group-theoretic formulation, both for deterministic and for randomized dynamics. This indicates a way to directly extend the robustness and randomization properties of consensus-type algorithms to more fields of application.