Mean square average consensus over directed communication topology with measurement noises

Average consensus is an interesting research topic and has wide applications in distributed control, estimation and optimization. Most existing studies are focused on balanced communication graphs which may not be practical. On the other hand, measurement noises are unavoidable in the real systems. Therefore, we consider the average consensus problem for multi-agent systems with measurement noises under unbalanced digraphs. By introducing extra variables to calculate the asymptotic weighting, the system matrix is scaled with the extra variables and the average of the initial state values can be asymptotically achieved. On the other hand, we introduce a decaying gain function such that the measurement noises can be attenuated. Due to the existence of noises, the average consensus is analyzed in the mean square sense. Finally numerical examples are given to demonstrate the proposed control protocol.