Multi-adaptive event-triggered consensus of positive multi-agent systems using pinning strategy

This paper investigates the multi-adaptive event-triggered consensus of positive multi-agent systems. First, two classes of event-triggered mechanisms are designed for leaders and followers, respectively. A multi-adaptive event-triggered pinning control protocol is proposed by virtue of the presented mechanisms. Compared to existing event-triggered pinning strategies, the proposed method further reduces communication costs and resource consumption. By using the matrix decomposition technique and linear programming approach, the gain matrices of the control protocol and sufficient conditions are constructed to ensure the positivity and consensus of the systems. The multi-adaptive event-triggered pinning control protocol is then extended to observer-based control scenarios, where pinning observers for both the leader and follower are designed separately, further reducing the update frequency of the observer. Moreover, the adaptive technique and event-triggered mechanism are combined to reduce the length of the triggering interval, thereby further conserving the overall system resources. Meanwhile, a bound for the minimum event-triggering interval is derived, which analytically proves the exclusion of Zeno behavior. Finally, the effectiveness of the results is verified via an illustrative example and comparative simulations.