Analysis of the Effects of Communication Trust and Delay on Consensus of Multi-Agent Systems

This research analyzes the effects of communication delay and trust in multi-agent systems (MAS). Consensus is a key attribute in the analysis of the stability of MAS systems. Communication and cooperation amongst the agents are major factors leading to the consensus of the system. Delay presents issues in the achievement of synchronization between the agents within the system that requires consistent and continuous communication. The effects of disturbances such as data loss and system lagging has to be analyzed properly. This paper presents a method for analysis of the stability of delayed MAS utilizing graph theory and the incorporation of the Laplacian matrix. The Lambert W function-based approach is used to solve the delay differential equations, which has an infinite number of roots caused by the delay operator. The method provides the capability to analytically solve the delay differential equations through computation of the eigenvalues, or characteristic roots, of the system to analyze stability. The convergence speed of the system is then modeled using MATLAB/Simulink. The delay in the system is varied from 0.1 second to 1 second to compare and analyze the stability and rate of convergence with respect to delay. Lastly, an analysis on the effects of communication trust between agents is examined and analyzed to tune out noise.