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

According to the practical application of multi-agent systems, a dynamic event-triggered predefined-time consensus algorithm is proposed for nonlinear multi-agent systems in this paper. First, the input controller of the agent is designed by utilizing a time-varying function to ensure the realization of the predefined-time consensus, and then the measurement error including a hyperbolic tangent function is proposed to exclude the occurrence of Zeno behavior. Finally, a trigger function is designed according to the measurement error, and internal dynamic variables are introduced to propose a dynamic event-triggered control protocol, which can ensure the reduction of triggering frequency. In view of the widespread existence of nonlinear systems in practical application scenarios, the control algorithm based on the first-order nonlinear multi-agent system designed in this paper is more general. For the predefined-time control algorithm, the time-varying function is introduced to ensure the system can achieve consensus at the predefined time. Compared with the traditional finite-time control algorithms 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 according to the actual needs of users, so the predefined-time control algorithm reduces the computation complexity and ensures the control accuracy to a great extent. In order to further reduce the triggering times, this paper introduces a new dynamic variable on the basis of the existing static event-triggered control algorithm, and an improved dynamic event-triggered control algorithm is designed. The dynamic variables can be adjusted in real-time with the systems and are always greater than 0. By the dynamic event-triggered mechanism proposed in this paper, the triggering frequency is greatly reduced, and Zeno behavior can be eliminated. Hence, the dynamic event-triggered control algorithm plays an important role in reducing the number of controller updates and actuator wear. Above all, the dynamic event-triggered predefined-time consensus algorithm proposed in this paper can not only guarantee the convergence speed, but also reduce the update frequency of the controller, and eventually realize the consensus in a predefined time without Zeno behavior existence. As the control input and measurement error are proposed by utilizing the hyperbolic tangent function, and the hyperbolic tangent function can solve non-differential problems caused by discontinuous functions, so the non-differential problems can be excluded. Moreover, the communication loop problem and singular problem also can be avoided in this paper. Finally, the effectiveness of the proposed dynamic event-triggered predefined-time consensus algorithm and theoretical analysis results are verified by numerical simulation.