Multi-Agent Formation with Aperiodic Sampling: A Hybrid System Framework

This work focuses on fixed-time formation problem of multi-agent systems with limited network bandwidth. The formation system based on kinematics equations of the agents is considered with a virtual leader. To deal with the communication with limited bandwidth, an aperiodic sampling mechanism based on an event-triggering condition is designed, in which estimate information of the agents are used. Then, a state estimator based on event-triggered measurements is developed to update the agents' estimate information. Considering the performance of fixed-time formation, a distributed practical fixed-time control protocol is presented base on the estimators, by which the time-varying formation in an approximately fixed-time can be reached. Subsequently, an auxiliary variable is introduced such that a hybrid system model that includes both flow dynamics and jump dynamics can be established. Then, a hybrid system framework is proposed for convergence analysis of the formation system. Additionally, design methods of formation parameters are offered to stress the usage of the formation with an aperiodic sampling. Finally, numerical simulations are provided to validate the effectiveness of the theoretical result.