Fixed-time Dynamical Pinning Control Of Multi-agent Systems With Disconnected Topology

A multi-agent system refers to a collection of individual agents that are able to perceive their environment and respond appropriately based on their own knowledge,in order to maintain coordination with other agents.Multi-agent systems have characteristics such as coordination,high fault tolerance,diversity,autonomy,and simplicity in design.Many groups in real life can be abstracted as agents,and multiagent systems can be used to replace artificial systems,which can not only save costs but also achieve overall system optimization through coordinated control.Therefore,it has received widespread attention in many areas and has potential application value.In practical problems,the motion of agents in a multi-agent system can be subject to external interference or attacks,which often causes agents to disconnect from the system,making the connectivity assumption in current research unable to be satisfied.Network disconnectedness poses a challenge for the control and collective behavior of multi-agent systems.In this paper,we consider the problem of fixed-time consensus control for second-order multi-agent systems under network topology disconnectedness.By combining observer and controller design,a new fixed-time consensus dynamic pinning control is proposed to address the network disconnectedness problem and achieve global system consensus.The main contributions of this paper are:(1)the proposal of a local dynamic pinning control strategy.When the network topology is disconnected,the system’s isolated agents are connected with information agents using local pinning methods to achieve network connectivity.(2)The study of fixed-time consensus for second-order multi-agent systems.Under network topology disconnectedness,the observer is designed to prove that the estimated state of the agents can converge to the leader’s state,and an upper bound for the estimated state convergence time is obtained.(3)Based on the designed observer,a system controller is constructed to achieve agent convergence to the leader within a fixed time,with the estimated state of the observer as an intermediate medium,and an upper bound for the system convergence time is obtained.By proof,it is shown that the constructed Lyapunov function is bounded and can achieve global convergence within a fixed time.