On Compensating Actuator Delays in Consensus Control under Undirected Graphs

This paper studies delay compensation in consensus control under undirected graphs via output feedback. The dynamics of each node involved in the network is subject to unknown bounded actuator delays. A transport partial differential equation (PDE) is employed to model the dynamics of the delay state, and a filter with adaptive control gains is proposed using the available relative output information of neighboring nodes. Based on the state of the filter, the estimation delay state, and the delay estimation, we propose two distributed adaptive output feedback consensus protocols. The first one employs a delay-adaptive predictor and guarantees local consensus, while the second one, replacing the delay estimation by a constant, is proven to be a global consensus controller provided that the delay mismatch is in a small compact set. Simulation results performed on a group of neutrally stable systems are presented to validate the effectiveness of the proposed scheme.