Adaptive dynamic event-triggered cluster consensus for second-order delayed MASs with input saturation

In this paper, the cluster consensus problem of second-order multi-agent systems (SOMASs) is investigated in which cooperative-competitive interactions among agents, input time delay, and input saturation are involved simultaneously. A novel adaptive dynamic event-triggered control (ETC) protocol is first designed to realize cluster consensus. Since the constant in static trigger condition is replaced by a dynamic parameter, the new control scheme can reduce the trigger times and save energy consumption. Then, switching topology problem of heterogeneous multi-agent systems (MASs) is also discussed based on the dynamic ETC strategy. Some sufficient conditions for achieving the cluster consensus of SOMASs are proposed by utilizing the Lyapunov stability theory and algebraic graph theory. Especially, to solve the saturation problem, Lagrange mean value theorem is adopted. Moreover, it is also proved that no Zeno behavior occurs under the proposed control protocol. Finally, two examples justify the significance of our theoretical results.