Distributed real-time optimization of average consensus

Distributed average consensus (DAC) algorithm is widely used in many applications. It utilizes matrix iteration to find the dominant eigenvector. To minimize the required number of iterations, the algorithm needs to be optimized. However, this optimization needs the knowledge of network topology, which is very hard to obtain for an individual agent in distributed networks. Thus, optimal step length and forgetting factor need to be calculated offline and forwarded to every agent. To solve this problem, we proposed a distributed real-time optimization technique so that each node can estimate these optimal parameters individually. In addition, the method is based on constant first-order DAC itself, so it will not stop the consensus process. The result shows that a numerical error due to quantization would exist in the distributed solution. It will increase as the network becomes larger. Thus, a numerical technique is introduced to mitigate the error. The estimated parameters after mitigation do not obviously decline the performance of higher-order DAC when network size is smaller than a threshold.