This paper continues our previous consensus scheme with only group information when neither absolute states nor inter-agent relative states are available, by considering two special nonlinear cases, L_∞-norm and L₂-norm. In the scheme, all the agents are partitioned into two subgroups at each time by certain probability, and then use the relative group information that concerns all agents’ states inside for state updating process. It is then shown that almost sure consensus can be achieved under the proposed scheme in both discrete time and continuous time for the two nonlinear cases. When for L_∞-norm group information, almost sure consensus is achieved if and only if the weighting parameter is greater than one in discrete-time case, and the weighting parameter is positive in continuous-time case. When for L₂-norm group information, the sufficient conditions to guarantee system consensus almost surely are the weighting parameter greater than $\sqrt{n}/2$ and positive in discrete-time case and continuous-time case, respectively. Finally, numerical simulations are proposed to validate the theoretical results.

本文延续了我们，只有组信息之前的共识方案时，既没有绝对的状态，也没有代理间相对状态可用，考虑两个特殊的非线性的情况下，大号_∞范数和大号₂范数。在该方案中，所有代理每次都以一定概率被分为两个子组，然后使用与内部所有代理状态相关的相对组信息进行状态更新过程。然后表明，在两种非线性情况下，在所提出的方案下，在离散时间和连续时间内，几乎可以肯定地达成共识。当大号_∞-规范组信息，并且仅当在离散时间情况下加权参数大于1且在连续时间情况下加权参数为正时，才能几乎确定共识。对于L _2-范数组信息，几乎可以肯定地确保系统共识的充分条件是权重参数大于$\sqrt{ñ}/2$在离散时间情况和连续时间情况下分别为正。最后，通过数值模拟验证了理论结果。