TY - GEN

T1 - On the steady-state range of averaging dynamics

AU - Bolouki, Sadegh

AU - Nedic, Angelia

AU - Basar, Tamer

N1 - Funding Information:
This Research was supported in part by the U.S. Air Force Office of Scientific Research (AFOSR) MURI grant FA9550-10-1-0573, by the National Science Foundation (NSF) grant DMS-13-12907, and by the Office of Naval Research (ONR) grant N00014-12-1-0998.
Publisher Copyright:
© 2016 American Automatic Control Council (AACC).

PY - 2016/7/28

Y1 - 2016/7/28

N2 - The steady-state range, or simply the range, of a network of multiple agents with fixed initial conditions refers to the intersection of all convex subsets of the state space, each containing all agent states as time grows. The notion of range is similarly defined for a subset of agents. Given the update rule of a network with unknown initial conditions, a subset of agents is said to be range-defining if, for any initial conditions, its range equals the range of the whole network. If, in addition, the subset remains range-defining regardless of its members' update rules-in the sense that the agents in that subset may or may not abide by their own update rules- the subset is said to be range-deciding. In this paper, minimal range-defining/-deciding sets given a general linear averaging update rule, which is uniquely characterized by a sequence of row-stochastic matrices, are investigated. More specifically, convergence properties of the sequence are employed to obtain a minimal range-defining/-deciding set and its size.

AB - The steady-state range, or simply the range, of a network of multiple agents with fixed initial conditions refers to the intersection of all convex subsets of the state space, each containing all agent states as time grows. The notion of range is similarly defined for a subset of agents. Given the update rule of a network with unknown initial conditions, a subset of agents is said to be range-defining if, for any initial conditions, its range equals the range of the whole network. If, in addition, the subset remains range-defining regardless of its members' update rules-in the sense that the agents in that subset may or may not abide by their own update rules- the subset is said to be range-deciding. In this paper, minimal range-defining/-deciding sets given a general linear averaging update rule, which is uniquely characterized by a sequence of row-stochastic matrices, are investigated. More specifically, convergence properties of the sequence are employed to obtain a minimal range-defining/-deciding set and its size.

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U2 - 10.1109/ACC.2016.7526684

DO - 10.1109/ACC.2016.7526684

M3 - Conference contribution

AN - SCOPUS:84992091979

T3 - Proceedings of the American Control Conference

SP - 6447

EP - 6452

BT - 2016 American Control Conference, ACC 2016

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2016 American Control Conference, ACC 2016

Y2 - 6 July 2016 through 8 July 2016

ER -