A novel fully distributed discrete-time min-max consensus seeking algorithm with high convergence speed

In this paper, we propose a novel discrete-time consensus algorithm based on the new min-max criterion for the discrete-time second-order linear agents. To boost the convergence speed, the proposed algorithm allocates three different operating modes to the network agents. Unlike most of the existing consensus algorithms in which the links of the communication graph have specific weights and these weights are required to have positive lower bounds to achieve asymptotic convergence, the communication graph in this paper has unspecific link weights. Accordingly, because of data transmission errors and faults, the weights of the communication links can even go from a positive to a negative value. Thus, the proposed algorithm can bring the agents to consensus under more general conditions. To demonstrate the efficacy of the proposed algorithm, numerical simulations are performed, and their results are compared with those of the minimum consensus algorithm, which shows a significantly faster convergence speed.