Lead-time Consensus Algorithm For Multi-agent Systems

Multi-agent systems research is currently a hot research direction.On the one hand,because of the rapid development of science and technology,especially the continuous breakthroughs in computer technology,automatic control,network communication and other fields,the research of multi-agent system can be transformed from theory to the real-world applications.On the other hand,it is also because an effective and flexible solution is urgently needed for increasingly stringent realworld requirements.Multi-agent systems can effectively overcome the shortcomings of a single agent such as waste of resources,difficult coordination,and complex operations.In scenarios such as airspace patrols and precision strikes,multi-agent systems can play great value and complete tasks efficiently.Consistency is a key problem in the study of multi-agent systems,and a suitable consensus control algorithm can make the states of multiple agents the same.Among them,the convergence speed is a key performance index to measure the control effect of the consensus control algorithm.The research on the convergence speed of the control algorithm has experienced great development from asymptotic-time,finite-time,fixed-time to prescribed-time.The prescribed-time control algorithm can make the system stable in any given prescribed time,and this prescribed time has nothing to do with the initial states and control parameters of the system,and it has received widespread attention once it was proposed.However,in the further study of the prescribed-time control algorithm,it is found that when the system is complex or there are complex disturbances,the system state will suddenly increase near the prescribed-time point,which will bury safety hazards for practical applications.Through the analysis of the jump problem,it is found that the main reason is that there is a small error between the system state and the target state near the prescribed-time point,and the control gain at this point tends to infinity.The multiplication of the two factors leads to a sudden increase in the control input.In order to solve this problem,some scholars have proposed a lead-time control algorithm,the core idea of which is to advance the stability time of the system.And a new type of time-varying measurement function is designed,which can make the controller switch before the prescribed-time point.The lead-time control algorithm can make the system stable within the prescribed-time without jumping.This paper is a research based on the existing results of the leadtime control algorithm.The main contributions and innovations are as follows:(1)In order to solve the jump problem in the prescribed-time control algorithm in the complex multi-agent systems,this paper proposes a lead-time average consensus control algorithm for the first-order multi-agent systems.In this paper,a new type of time-varying measurement function is constructed,and a lead-time average consensus controller is designed.At the same time,two estimation methods for the upper limit of the convergence time of the systems are proposed.The final systems can achieve average consistent within any given prescribed time without jumping problem.(2)In this paper,the lead-time control algorithm is extended to the second-order system,and a lead-time control algorithm for the second-order system with disturbance is designed based on the adding a power integrator method.The control algorithm designed by using the power integral discriminant method is mainly the result of finite time,which is extended in this paper.A power integral error function with a time-varying measurement function is designed,and a detailed stability analysis is carried out in combination with a Lyapunov function with a power integral term.Under the control algorithm proposed in this paper,the second-order system can be stable and has good antidisturbance performance in any given time.(3)Based on the adding a power integrator method,this paper designs a lead-time consensus control algorithm for second-order multi-agent systems.For the multi-agent systems,a time-varying measurement function is designed,and combined with this function,the target state function of the systems and the power integral error function under the multi-agent systems are constructed.The Lyapunov function with power integral term is given,and it is divided into two stages before the prescribed time and after the prescribed time for consistency analysis.The final designed lead-time control algorithm can make the multi-agent systems consistent within a prescribed time,and the prescribed time has nothing to do with the initial states of the systems and control parameters.