The behavior of heterogeneous multi-agent systems is studied when the coupling matrices are possibly all different and/or singular, that is, its rank is less than the system dimension. Rank-deficient coupling allows exchange of limited state information, which is suitable for the study of multi-agent systems under output coupling. We present a coordinate change that transforms the heterogeneous multi-agent system into a singularly perturbed form. The slow dynamics is still a reduced-order multi-agent system consisting of a weighted average of the vector fields of all agents, and some sub-dynamics of agents. The weighted average is an emergent dynamics, which we call a blended dynamics. By analyzing or synthesizing the blended dynamics, one can predict or design the behavior of a heterogeneous multi-agent system when the coupling gain is sufficiently large. For this result, stability of the blended dynamics is required. Since stability of the individual agent is not asked, the stability of the blended dynamics is the outcome of trading off the stability among the agents. It can be seen that, under the stability of the blended dynamics, the initial conditions of the individual agents are forgotten as time goes on, and thus, the behavior of the synthesized multi-agent system is initialization-free and is suitable for plug-and-play operation. As a showcase, we apply the proposed tool to four application problems; distributed state estimation for linear systems, practical synchronization of heterogeneous Van der Pol oscillators, estimation of the number of nodes in a network, and a problem of distributed optimization.
翻译:当混合矩阵可能是所有不同和(或)单一的,即其级别低于系统维度时,就会研究多种多试剂系统的行为。 等级缺失的组合可以交换有限的国家信息, 这适合于在产出混合下研究多试剂系统。 我们提出协调变化, 将多元多试剂系统转换成一种奇而不稳定的形式。 缓慢的动态仍是一个减少的多试剂系统, 由所有代理剂的矢量字段和一些代理剂的次动力学的加权平均值构成。 加权平均是一种新兴动态, 我们称之为混合动态。 通过分析或合成混合动态, 人们可以预测或设计混合多试剂系统的行为, 而当混合的多试剂系统获得足够大的收益时。 为了这个结果, 混合的动力系统需要稳定。 由于单个代理剂的稳定, 混合的动态的稳定性是代理剂中实际稳定性交易的结果。 可以看到, 在混合动态稳定的情况下, 我们称之为混合动态的动态的初始条件, 通过合成的混合动态, 各个代理剂的最初条件和预估量系统被遗忘了。