Event-Based Sampled-Data Average Consensus

This study addresses one of the most essential distributed control problems in multiagent systems, called the average consensus issue, using a new event-triggered sampling control perspective. Although the continuous-time sampling for average consensus has provided good results currently, a systematic investigation into the continuous-time agent dynamics with sampled-data control inputs under an event-triggered mechanism is critically lacking. The problem considered in this paper can be formulated into an average consensus problem of hybrid systems. The method considers three types of control schemes, among which periodic sampling is integrant. The first scheme is a classical sampling controller reinvestigated through a lemma. The second scheme realizes aperiodic control update as well as periodic communication, while the third scheme achieves both aspects aperiodically. Corresponding sufficient conditions of the aforementioned three schemes are derived such that the asymptotic stability of systems is ensured by using algebraic graph theory, matrix analysis, and Lyapunov theory. The constraints for the allowed sampling period, event parameter, and maximum eigenvalue of graph Laplacian are explicitly derived. Moreover, the potential Zeno behavior of agents due to the sampling control theory is avoided. Thus, a digitally implementable technique is provided. Finally, some numerical examples are provided to verify the effectiveness of the proposed theoretical analysis.