Average Consensus in Discrete-Time Cyclic Pursuit with Communication Delays

In this paper, the problems introduced by homogeneous communication delay in a discrete average consensus rendezvous problem are investigated. First, we have shown that the amount of communication delay does not affect the system's stability conditions, as the conditions remain the same for delays ranging from zero to any arbitrary finite value. The deviation in the final convergence point due to communication delays from that of the ideal no-delay situation is studied. Based on this, we introduce a margin on the value of gain to keep this deviation in a predefined bound. In an attempt to maintain the deviation in a pre-defined bound, with an increase in communication delay, the system becomes sluggish as the gain needs to be reduced. Also for the same communication delay as the deviation bound reduces, the gain needs to be reduced due to which the system convergence also becomes sluggish. After finding out the gain corresponding to the fastest convergence, we use it to build an estimator with the help of which the agents can reach the average consensus without any deviation even in the presence of communication delay. We also estimate the amount of delay in the communication links in case of an unknown delay.