A group behavior of a heterogeneous multi-agent system is studied which obeys an "average of individual vector fields" under strong couplings among the agents. Under stability of the averaged dynamics (not asking stability of individual agents), the behavior of heterogeneous multi-agent system can be estimated by the solution to the averaged dynamics. A following idea is to "design" individual agent's dynamics such that the averaged dynamics performs the desired task. A few applications are discussed including estimation of the number of agents in a network, distributed least-squares or median solver, distributed optimization, distributed state estimation, and robust synchronization of coupled oscillators. Since stability of the averaged dynamics makes the initial conditions forgotten as time goes on, these algorithms are initialization-free and suitable for plug-and-play operation. At last, nonlinear couplings are also considered, which potentially asserts that enforced synchronization gives rise to an emergent behavior of a heterogeneous multi-agent system.

翻译：正在研究一个符合“ 单个矢量字段平均值” 的多元多试剂系统的集团行为。 在平均动态稳定( 不要求单个代理物的稳定 ) 下, 各种多试剂系统的行为可以通过平均动态的解决方案来估计。 以下的想法是“ 设计” 单个代理物的动态, 以便平均动态能完成所期望的任务。 讨论的一些应用包括估计网络中的代理物数量, 分布最小平方或中位求解器, 分布优化, 分布状态估计, 以及组合振荡器的强大同步。 由于平均动态的稳定性使得最初被遗忘的条件随着时间的流逝, 这些算法是没有初始化的, 适合插接和玩操作。 最后, 还考虑到非线性联动, 这可能表明强制同步会产生多种多试剂系统的突发行为 。