Discrete-time function consensus algorithms for second-order moment statics

This paper studies distributed function calculation by discrete-time consensus algorithms. We propose a class of discrete-time recursive algorithms to calculate the weighted second-order moment statics in a distributed way. Different from the continuous-time algorithm, the jumping of the states in discrete-time algorithms makes the convergence analysis much more difficult. In this paper, we first give some sufficient conditions on the control input for driving the whole system to function consensus. Then based on the conditions, we design the algorithm and show that if the communication topology is connected, then by adjusting the communication gain between adjacent agents properly, the proposed distributed algorithm can drive all agents´ states to the square root of the weighted second-order moment statistics of the initial values. The numerical simulation shows the effectiveness of our algorithms.