We consider a multi-agent system where agents aim to achieve a consensus despite interactions with malicious agents that communicate misleading information. Physical channels supporting communication in cyberphysical systems offer attractive opportunities to detect malicious agents, nevertheless, trustworthiness indications coming from the channel are subject to uncertainty and need to be treated with this in mind. We propose a resilient consensus protocol that incorporates trust observations from the channel and weighs them with a parameter that accounts for how confident an agent is regarding its understanding of the legitimacy of other agents in the network, with no need for the initial observation window T0 that has been utilized in previous works. Analytical and numerical results show that (i) our protocol achieves a resilient consensus in the presence of malicious agents and (ii) the steady-state deviation from nominal consensus can be minimized by a suitable choice of the confidence parameter that depends on the statistics of trust observations.

This letter studies the Friedkin-Johnsen (FJ) model with diminishing competition, or stubbornness. The original FJ model assumes that each agent assigns a constant competition weight to its initial opinion. In contrast, we investigate the effect of diminishing competition on the convergence point and speed of the FJ dynamics. We prove that, if the competition is uniform across agents and vanishes asymptotically, the convergence point coincides with the nominal consensus reached with no competition. However, the diminishing competition slows down convergence according to its own rate of decay. We study this phenomenon analytically and provide upper and lower bounds on the convergence rate. Further, if competition is not uniform across agents, we show that the convergence point may not coincide with the nominal consensus point. Finally, we evaluate our analytical insights numerically.