Research On Prescribed-time Consensus Of Multi-Agent Systems Under Prescribed Performance

With the development of artificial intelligence,the relevant algorithms of multi-agent systems have become an important tool for realizing intelligence and solving collaborative problems.In a multi-agent system,agents share information and cooperate with adjacent agents to solve problems that cannot be solved by a single agent.This kind of collaborative control is widely used in cluster control,swarm control,aggregation control,network estimation and other fields.The consensus problem is a classic problem in the cooperative control of multi-agent systems.Its core is to design a suitable control strategy to make the states of all agents tend to be consistent.The convergence rate is an important indicator of the consensus speed.At present,the results of research on the consensus convergence rate of multi-agents mainly focus on asymptotic time convergence,finite time convergence and fixed time convergence.These convergence algorithms have certain limitations.Researching a faster and easier-to-design convergence algorithm has become a difficult problem in the study of convergence rate.In addition,in the consensus problem,some transient performance and steady-state performance of the system(such as overshoot,undershoot,and steady-state error)have clear requirements in practical applications.How to ensure the prescribed performance of the system while achieving consensus in the multi-agent system is a focus of multi-agent system research.Therefore,this paper closely focuses on these two issues.The main contributions and innovations are as follows:(1)For the ordinary second-order system,a prescribed time convergence controller is designed using the backstepping method,so that the system can achieve convergence within a predetermined time;extend this prescribed time convergence algorithm to the second-order multi-agent system to achieve the consensus of the system’s position state and velocity state.The designed multi-agent consensus algorithm is a distributed result(2)Aiming at the problem that the speed state eventually converges to zero when using the backstepping method to achieve consensus,this paper redesigns a new virtual input to ensure that the sum of the speed states remains unchanged when the system converges.The proof and analysis show that,regardless of the system disturbance,under the action of the new fully distributed prescribed time consensus control algorithm,the position state and velocity state of the system can achieve average consensus.(3)Aiming at the requirements of prescribed performance in multi-agent systems,this paper combines the prescribed time stability theory and prescribed performance control strategy,and a prescribed time consensus controller for multi-agent systems with prescribed performance is designed.First,a new performance function is designed to ensure that the position state of the multi-agent system always moves within the specified range;secondly,a transfer function is introduced to transform the range limit of the motion state into a convergence problem of a new error function;finally,the system state coupled with the performance function,the prescribed time controller of the multi-agent system under the prescribed performance based on the error function is designed.