Second-order distributed consensus with modified probabilistic quantization

In order to improve the accuracy of distributed consensus under quantized communication, in the paper, we firstly propose a modification to the probabilistically quantized distributed (PQDA) algorithm, and we update the state of every node by its state and the probabilistically quantized information of the adjacency nodes. Moreover, based on the modification, we propose a second-order modified probabilistically quantized algorithm. We analyze the performance and the mean square errors of the second-order modified probabilistic quantization distributed consensus, by analysis and simulation, the results show the second-order distributed consensus with modified probabilistic quantization fails to reach a consensus, but the mean square error is far smaller than that of the PQDA algorithm, and the curve chart of the new algorithm is similar to that of the distributed average consensus algorithm without distortion.