Average consensus with minimum energy consumption: Optimal topology and power allocation

Consensus algorithms have generated a lot of interest due to their simplicity in computing globally relevant statistics exploiting only local communications among sensors. However, the inherent iterative nature of consensus algorithms makes them prone to a possibly large energy consumption. Because of the strong energy constraints of wireless sensor networks, it is then of interest to minimize energy consumption necessary to achieve consensus, within a prescribed accuracy requirement. In this work, we propose a method for optimizing the network topology and power allocation over each link, in order to minimize energy consumption, while ensuring that the network reaches a global consensus. Interestingly, we show how to introduce a relaxation in the topology optimization that converts a combinatorial problem into a convex-concave fractional problem. The results show how the sparsity of the resulting network depends on the propagation model.