Resilient Consensus for Robust Multiplex Networks with Asymmetric Confidence Intervals

The consensus problem with asymmetric confidence intervals considered in this paper is characterized by the fact that each agent can have optimistic and/or pessimistic interactions with its neighbors. To deal with the asymmetric confidence scenarios, we introduce a novel multiplex network presentation for directed graphs and its associated connectivity concepts including the pseudo-strongly connectivity and graph robustness, which provide a resilience characterization in the presence of malicious nodes. We develop distributed resilient consensus strategies for a group of dynamical agents with locally bounded Byzantine agents in both continuous-time and discrete-time multi-agent systems. Drawing on our multiplex network framework, much milder connectivity conditions compared to existing works are proposed to ensure resilient consensus. The results are further extended to cope with resilient scaled consensus problems which allow both cooperative and antagonistic agreements among agents. Numerical examples are also exhibited to confirm the theoretical results and reveal the factors that affect the speed of convergence in our multiplex network framework.

Automated summary

This paper addresses the consensus problem with asymmetric confidence intervals, introduces a novel multiplex network presentation, and develops distributed resilient consensus strategies to ensure resilience in the presence of malicious nodes. The results provide milder connectivity conditions compared to existing works and are extended to cope with resilient scaled consensus problems, allowing for both cooperative and antagonistic agreements among agents. Numerical examples confirm the theoretical results and reveal factors affecting the speed of convergence in the multiplex network framework.