Consensus-based Predefined-time Coordinated Control Of Multi-agent System

A variety of disciplines such as biology,sociology,statistics,computer science and control engineering began to merge with the advancement of society and development of science.A new research interest,namely control of multi-agent system emerged.With the acceleration of the calculation ability of micro chips and the promotion of 5G communication technology,the scale of current control systems is becoming larger and larger.Multi-agent systems are generally distributed and networked systems,which contains many independent subsystems,and the volume of communication is huge.The number of subsystems in the whole system maybe changed based on the requirement of the application.In traditional centralized control,all communications during the control process need to be transmitted through the central host.The system has poor flexibility and low robustness.Therefore,the use of centralized control in multi-agent coordinated control cannot meet the requirements,so distributed control is the best choice.How to solve the consensus problem of multi-agent systems is the prerequisite for solving other problems.Consensus-based control has been widely used in the fields of satellite attitude coordination,large-scale sensor networks,and multi-agent cooperative transformation.In real life,many applications have strict requirements on the convergence time of the system.The convergence time is an important indicator for judging a control algorithm.Thus,it is necessary to design a control algorithm to drive the multi-agent system to reach consensus as quickly as possible.How to design distributed control algorithms that can drive the multi-agent systems reach consensus within a limited time is a hot topic in this field.This paper mainly focus on designing distributed consensus control algorithms with a predetermined convergence time.In the first place,a distributed control protocol for a first-order multi-agent system was designed,which could drive the system to reach consensus within a predetermined time and can guarantee that each agent can track external signals or the trajectory of a virtual leader.The time for the tracking error to converge to zero is bounded.The upper bound of the time is only related to one parameter in the control protocol,independent of the communication topology of the system or system structure.By tuning this parameter,the convergence time of the tracking error can be adjusted.For the second-order multi-agent system with external uncertain disturbances,the design of predefined-time consensus-based tracking control algorithm is studied.First,a nonlinear sliding manifold is designed,and then a control law is designed which can force the tracking error reach the sliding surface within a predetermined time.When the error trajectory arrives,it remains on the sliding surface while sliding to zero within a predetermined time.The stability of the designed control law is proved utilizing algebraic graph theory,matrix inequality and Lyapunov theory.For a multiple nonholonomic wheeled mobile robot system,a predetermined time formation tracking control algorithm is derived.The nonholonomic system is decomposed through a reversible coordinate transformation technique,and then a distributed observer which can estimate the leader input and state in a predetermined time is designed for each follower robot.All robots can accurately observe the input signal and current state of the virtual leader after the observer error converges.Based on observed value,the control law is designed.This method can ensure that the robot system form a preset geometry shape within a predetermined time and the formation center track the trajectory of the virtual leader at the same time.Finally,with the help of graph theory,matrix inequality theory and Lyapunov theory,the effectiveness of the designed observer and control algorithm is proved.