Asymptotic Consensus on the Average of a Field for Time-Varying Nonlinear Networks Under Almost Periodic Connectivity

The paper presents new results on asymptotic consensus for continuous time nonautonomous nonlinear networks under almost-periodic interactions. We introduce such consensus algorithms in order to estimate the average 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 exploited, frozen in state variables, and of simple verification, thanks to ergodicity of the underlying agents' spatial dynamics. In the considered setup, consensus variables are different than those affecting network's connectivity unlike most of the existing literature on asymptotic agreement. The application of the proposed results is illustrated considering two representative examples in the scenario of autonomous sampling by mobile sensor agents.