Consensus of time-varying nonlinear non-autonomous networks with application to field sampling by mobile robots

The paper presents new results on asymptotic consensus for continuous time non-autonomous nonlinear networks under almost-periodic interactions. We treat consensus variables that are different than those affecting network´s connectivity and allow the former to track an estimate of the average magnitude of a measured field despite the presence of limited agents´ interaction (herein represented by almost periodic connectivity). To this end, a suitable notion of integral connectivity is introduced, frozen in state variables, and of simple verification, without requiring monotonicity of interactions (viz. network´s cooperativity). An application of the proposed results is illustrated considering a representative example in the scenario of autonomous sampling by mobile robots.