Abstract:A novel hybrid event-triggered fixed-time consensus control method based on backstepping is proposed for second-order multi-agent systems with unknown disturbances under arbitrary switching topologies. Firstly, a new hybrid event-triggered mechanism that combines dynamic and static event-triggered conditions is presented. During the transient response phase of the system, a novel dynamic event-triggered condition is designed based on auxiliary variables" power terms, which can adaptively adjust the triggering threshold according to the evolution of the agents" measurement errors and velocity errors, thereby autonomously reducing the number of event triggers. During the steady-state response phase, a static event-triggered condition is employed with appropriate fixed thresholds to reduce unnecessary triggers in this phase, effectively overcoming the problem of triggering thresholds being too small after dynamic variables stabilize. Then, using multiple common Lyapunov functions, it has been proven through two stages that the proposed control method, along with sufficient consensus conditions, can achieve practical fixed-time consensus for second-order multi-agent systems under arbitrary switching topologies. Subsequently, it has been proven that Zeno behavior is excluded in the system by utilizing the differentiability of designed measurement errors that incorporate hyperbolic tangent functions. Finally, numerical simulation results validate the effectiveness and superiority of the proposed consensus control method.