Robust Distributed Estimation of the Maximum of a Field

This paper deals with the problem of robust distributed sampling of a field in the presence of unreliable sensors/agents. An algorithm is devised to estimate the maximum of the field over the domain spanned by the agents where some of the sensors can sample wrong measurements over a finite time, higher than the maximum field value. Necessary and sufficient conditions are given to guarantee convergence to the maximum field value and a robust and redundant algorithm design is presented by combining an exhaustive ergodic search with multiagent consensus protocols. In this original setup, the presence of unilateral interactions and exogenous signals is considered, the latter representing the measures sampled by the agents. Representative examples are presented to illustrate the effectiveness of the proposed framework and conditions.