Max-consensus using the soft maximum

A distributed consensus algorithm for estimating the maximum and the minimum of the initial measurements in a sensor network is proposed. Estimating extrema is useful in many applications such as temperature control. In the absence of communication noise, max estimation can be done by updating the state value with the largest received measurements in every iteration at each sensor. In the presence of communication noise, however, the maximum estimate may incorrectly drift to a larger value at each iteration. As a result, a soft-max approach together with a consensus algorithm is introduced herein. Soft-min based algorithm is also described using the same approach. It is shown that for some distributions of the initial measurements, a modified soft-min consensus can also be used to calculate the max. A shifted non-linear bounded transmit function is also introduced to improve the convergence speed. A trade-off between power of the transmitted signal and the error in the estimate is described and simulation results are provided.