Reach almost sure consensus via Lp-norm group information

Abstract

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 n/2 and positive in discrete-time case and continuous-time case, respectively. Finally, numerical simulations are proposed to validate the theoretical results.