Consensus-based algorithm for distributed estimation of the maximum of a field

This paper deals with the problem of distributed estimation of the maximum of a continuous scalar field by combining exhaustive ergodic search with multi-agent consensus protocols. In this original set-up, the presence of unilateral interactions and exogenous signals is considered, the latter representing the measures sampled by the agents and an algorithm is devised to estimate the maximum of the field over the domain spanned by the agents. Necessary and sufficient conditions are given to guarantee convergence to the maximum field value. Illustrative examples are presented to show the effectiveness of the proposed framework and conditions.