Distributed optimisation design with triggers for disturbed continuous‐time multi‐agent systems

A distributed optimisation problem is investigated for disturbed continuous‐time multi‐agent systems with discrete‐time communication and gradient measurement. First, a distributed optimisation algorithm with time‐triggered communication and gradient measurement is proposed. Then an event‐triggered communication strategy and an event‐triggered gradient measurement strategy are developed, and a distributed optimisation algorithm combining these two event‐triggered strategies is designed, in which the two event‐triggered strategies are free of Zeno behaviour. Moreover, the exponential convergence of system can be guaranteed by using the internal model design to reject the external disturbance. Finally, an example illustrates the effectiveness of the proposed algorithms.