Event-triggered fixed-time cooperative tracking control for uncertain nonlinear second-order multi-agent systems under directed network topology

In this work, we concern with the fixed-time event-triggered cooperative tracking control problem for uncertain nonlinear second-order multiagent systems (MASs) under directed communication topology. Firstly, to obtain fixed-time tracking control, a fractional-order-based nonlinear algorithm is designed. Secondly, based on our proposed fixed-time consensus tracking controller, an event-triggered mechanism is further developed to reduce the updating frequency of the controllers. Different from the finite-time control algorithm, the fixed-time strategy can achieve consensus tracking within a settling time regardless of the initial values. In addition, a strictly positive lower bound of the inter-event intervals is provided to demonstrate that the Zeno-behavior is avoided before the consensus tracking is achieved. Finally, several simulations are performed to illustrate the validity of the proposed algorithms.