Synchronization

Robust Synchronization of Uncertain Linear Multi-Agent Systems
Harry L. Trentelman⇤ and K. Takaba⇤⇤
⇤ Johann

Bernoulli Institute for Mathematics and Computer Science, University of Groningen, Groningen, The Netherlands. ⇤⇤ Department of Electrical and Electronic Engineering, College of Science and Engineering, Ritsumeikan University, Japan

MTNS Melbourne, 2012

Harry L. Trentelman and K. Takaba (Johann Bernoulli Institute for Uncertain Linear MTNS Melbourne, 2012 Robust Synchronization of Mathematics and Computer Science, University of 20 Multi-Agent Systems 1 / Gron

Outline

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Synchronization Robust synchronization Computation of robustly synchronizing protocols Guaranteed robust synchronization radius Future research

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Harry L. Trentelman and K. Takaba (Johann Bernoulli Institute for Uncertain Linear MTNS Melbourne, 2012 Robust Synchronization of Mathematics and Computer Science, University of 20 Multi-Agent Systems 2 / Gron

Synchronization of multi-agent systems

Agent dynamics
Multi-agent networks with p agents, undirected network graph, Laplacian L. Identical nominal dynamics of the agents: ˙ xi = Axi + Bui , yi = Cxi , i = 1, 2 . . . , p (A, B) is stabilizable, (C , A) is detectable. State xi 2 Rn , input ui 2 Rm , output yi 2 Rq Neighbouring set of agent i is Ni . Information of agent i about its neighbours is Âj2Ni (yi yj )

Harry L. Trentelman and K. Takaba (Johann Bernoulli Institute for Uncertain Linear MTNS Melbourne, 2012 Robust Synchronization of Mathematics and Computer Science, University of 20 Multi-Agent Systems 3 / Gron

Synchronization of multi-agent systems

Dynamic protocol
The synchronization problem is the problem of finding a protocol that makes the network synchronized. We consider dynamic protocols of the form ˙ wi = Awi + BF j2Ni  (wi

wj ) + G (

j2Ni

 (yi

yj )

Cwi ), ui = Fwi .

Structure of the protocol: combination of observer for the ith relative state Âj2Ni