We propose two distributed dynamic triggering laws and one predictive self-triggered algorithm to solve the consensus problem for multi-agent systems with event-triggered control. Compared with existing triggering laws, the proposed triggering laws involve internal dynamic variables which play an essential role to guarantee that the triggering time sequence does not exhibit Zeno behavior. Some existing triggering laws are special cases of our dynamic triggering laws. Unlike the great majority of existing works that propose distributed triggering laws and self-triggered algorithm, continuous listening is avoided in the proposed predictive self-triggered algorithm.

Under the condition that the underlying graph is undirected and connected, it is proven that the proposed dynamic triggering laws and the predictive self-triggered algorithm together with the event-triggered control make the state of each agent converges exponentially to the average of the agents’ initial states. Numerical simulations illustrate the effectiveness of the theoretical results and show that the dynamic triggering laws and the predictive self-triggered algorithm lead to reduction of actuation updates and inter-agent communications.