“Robustness of Synchronization of Heterogeneous Agents by Strong Coupling and a Large Number of Agents”

• published in IEEE Trans. on Automatic Control, Oct. 2016
• http://dx.doi.org/10.1109/TAC.2015.2498138
• Abstract: This technical note studies robustness of synchronization against heterogeneity of multi-agent systems. Here, heterogeneity also includes uncertainties and external disturbances in each agent. In order to effectively deal with the heterogeneous agents, we introduce the concept of the averaged dynamics which is the average of all agents’ dynamics, and then claim that two sources enhance the robustness of synchronized behavior against heterogeneity of agents’ dynamics. First, in spite of the heterogeneity of agents’ dynamics, we show that strong coupling among agents makes the trajectories of all agents arbitrarily close to the averaged dynamics. Second, in the averaged dynamics, the effect of variations in each agent gets smaller as the number of agents increases. Simulation results confirm the claim that a large number of agents with strong couplings have robust synchronization.

본 연구의 의의는 multi-agent system에 있어 heterogeneous한 개체들이 high gain coupling을 통해 연결되어 있을 때, 이러한 연결로부터 개별 개체의 동역학이 갖지 않은 새로운 동역학으로부터의 행동양태를 만들어 낼 수 있으며 (이를 emergent dynamic behavior라고 할 수 있음), 이 새로운 동역학을 “averaged dynamics” 혹은 “blended dynamics”라고 부르려고 한다.  이때 coupling gain을 더 높일 수록 개별 개체가 가진 uncertainty나 external disturbance에 둔감한 강인한 군집행동을 보일 수 있음을 수학적으로 보인 논문이다. 또한, 개별 시스템의 parameter가 확률을 가진 random variable로 주어진다고 할 때, 개체 숫자가 많아질 수도록 강인한 성질을 가짐을 보였다.

이러한 방향의 연구는

“Practical consensus for heterogeneous linear time-varying multi-agent systems”
J. Kim, J. Yang, J.S. Kim, and H. Shim
In Proc. of 12th Int. Conf. on Control, Automation and Systems (ICCAS), Jeju Island, Korea, pp. 23-28, 2012
Download: 12.ICCAS.Kim.PracCons

“On robustness of synchronization in heterogeneous multi-agent systems”
J. Kim, J. Yang, H. Shim, and J.S. Kim
In Proc. of 12th European Control Conf., Zurich, Switzerland, pp. 3821-3826, 2013
Download: 13.ECC.Kim

로부터 처음 시작되었다. 이후

“Robust synchronization for high-order heterogeneous multi-agent systems”
Jaeyong Kim and H. Shim
In Proc. of SWARM 2015: The First Int. Symp. on Swarm Behavior and Bio-Inspired Robotics, Kyoto, Japan, 2015, pp. 293-294

에서 고차 시스템으로 확장되었다.