Research On Prescribed-time Consensus For Second-order Multi-agent System

As a significant branch of distributed artificial intelligence,multi-agent system is mainly expected to solve complex practical problems through the cooperation between multiple simple agents,instead of a single complex system.Different from the traditional centralized control method,Distributed control method,dedicated to achieving a global common objective by using only local communication in the absence of central coordination,is more promising due to the advantages such as limited communication/sensing range,cooperative fashion,flexibility,and scalability.Research on distributed control of multi agent system has been widely used in formation control,aggregation control,swarm control,synchronization and coordinated decision control.Consensus is a classic issue in the field of distributed cooperative control of multi-agent system.The key is to design appropriate consensus protocol or algorithm to make each agent state tend to the same value.The convergence rate is an important performance to study the consensus problem for multi-agent system.At present,numerous existing research focus on asymptotic time,finite time and fixed time consensus control.In these research fields,two well-known and common technical challenges related to those issues are twofold: how to achieve the consensus with high accuracy in the desired time,and how to ensure consensus tracking in cases where only part of the subsystem has access to the leader's trajectory.Therefore,the main contributions and innovations of this paper could be summarized as follows:(1)On the basis of the system topology,a convex hull formed by leaders is constructed for second-order multi-agent system with multiple leaders and followers.Then,the distributed prescribed-time observer and the distributed lead-time observer are structured to estimate the information of the convex hull spanned by leaders in preassigned finite time.(2)Based on the convex hull state information obtained by the distributed observer,a novel scaling nonlinear function is designed to structure the prescribed-time containment control algorithm.Lyapunov candidate function is constructed,and through rigorous theoretical analysis and numerical simulation on MATLAB.We find that the followers could keep up with the convex hull formed by the leaders,where the convergence time can be preassigned arbitrarily under the prescribed-time containment control algorithm.The convergence stability time does not depend on the initial value of the system and other control parameters.(3)In order to avoid the sudden change at the certain time in the prescribed-time control algorithm,the lead-time stability control for first-order nonlinear continuous system is investigated,and the property analysis of disturbance rejection is given.The convergence time of the system under the proposed algorithm can be given as needed within any physically allowable range.Namely,the system achieves stability before the preassigned time,which does not depend on initial conditions or other controller parameters.Furthermore,the convergence error under the lead-time control algorithm can be reduced to an adjustable range for the system with disturbances,and it shows better robustness and disturbance rejection.