Singularly perturbed algorithms for dynamic average consensus

This paper proposes two continuous-time dynamic average consensus algorithms for networks with strongly connected and weight-balanced interaction topologies. The proposed algorithms, termed 1st-Order-Input Dynamic Consensus (FOI-DC) and 2nd-Order-Input Dynamic Consensus (SOI-DC), respectively, allow agents to track the average of their dynamic inputs within an O(ε)-neighborhood with a pre-specified rate. The only requirement on the set of reference inputs is having continuous bounded derivatives, up to second order for FOI-DC and up to third order for SOI-DC. The correctness analysis of the algorithms relies on singular perturbation theory for non-autonomous dynamical systems. When dynamic inputs are offset from one another by static values, we show that SOI-DC converges to the exact dynamic average with no steady-state error. Simulations illustrate our results.