Dynamic event-triggered predefined-time consensus for first-order nonlinear multiagent systems

To ensure fast convergence speed and save communication resources, a dynamic event-triggered predefined-time consensus algorithm is proposed for nonlinear multiagent systems in this study. First, the input controller of each agent is developed using a time-varying function to ensure the realization of the predefined-time consensus. Afterward, the measurement error, based on a hyperbolic tangent function, is proposed to exclude the occurrence of Zeno behavior. Finally, a trigger function is established based on the measurement error, and internal dynamic variables are introduced to propose a dynamic event-triggered control protocol, which can reduce triggering times. In view of the widespread presence of nonlinear systems in practical scenarios, the control algorithm based on the developed first-order nonlinear multiagent system is generalized. For the predefined-time control algorithm, a time-varying function is introduced to ensure that the system can achieve consensus at the predefined time. Compared with the conventional finite-time and fixed-time control algorithms, the upper bound of convergence time does not depend on the initial state, topology information, and control parameters but can be arbitrarily set in advance as per the actual needs of users. Thus, the predefined-time control algorithm reduces the computation complexity and ensures control accuracy to a great extent. To further reduce the triggering times, the dynamic event-triggered control algorithm is improved by introducing a novel dynamic variable based on the existing static event-triggered control algorithm. This dynamic variable can be adjusted in real-time with the systems and is always greater than 0. Using the proposed dynamic event-triggered algorithm greatly reduces the triggering times, and Zeno behavior can be eliminated. Therefore, the dynamic event-triggered control algorithm plays an important role in reducing the number of controller updates and actuator wear. Above all, the proposed dynamic event-triggered predefined-time consensus algorithm can not only ensure the convergence speed but also reduce the update frequency of the controller and eventually achieve the consensus in a predefined time without Zeno behavior. Because the control input and measurement error are developed by using the hyperbolic tangent function and the hyperbolic tangent function can solve nondifferential problems caused by discontinuous functions, the nondifferential problems can be excluded. Finally, the effectiveness of the proposed dynamic event-triggered predefined-time consensus algorithm and theoretical analysis results are confirmed using numerical simulations. To sum up, this dynamic event-triggered predefined-time consensus algorithm can ensure the consensus of first-order nonlinear mutiagent systems in arbitrary setting time, and reduce the trigger times, which is more likely to be applied to practical engineering.