Fixed-time Consensus Control Of Second-order Multi-agent Systems

Coordinated control of multi-agent systems is a popular research topic in recent decades,and its research results have been widely used in engineering fields such as UAVs formation flying,wireless sensor networks and multi-robot coordinated control.The consensus control is a branch research field of coordinated control of multi-agent systems.The control goal is to use local information through the consensus protocol between the agents to make all agents reach an agreement on a common state.The fixed-time consensus control requires all agents to achieve consensus within a fixed time,which is faster than traditional consensus control.In the practical engineering environment,disturbances and nonlinear dynamics will negatively affect the stability of multi-agent systems,and they are not negligible.In addition,due to the limited communication range of some agents,the design of the control protocol must ensure that the distance between neighbors does not exceed the maximum communication distance,thereby protecting the connectivity of communication topology from being damaged.This is the prerequisite of achieving consensus.It is challenging to study the fixed-time consensus of multi-agent systems,and to solve the problems of disturbances,nonlinear dynamics and connectivity preservation at the same time.The main research contents of this paper are as follows:(1)Aiming at the fixed-time consensus problem of second-order multi-agent systems with external disturbances under undirected topology,the control method of distributed observation and decentralized control is adopted.Distributed observer enables followers to estimate the leader's state within a fixed time.Decentralized sliding-mode controller can overcome external disturbances and enable followers to track the observer's observation within a fixed time,thereby achieving fixed-time consensus.At the same time,using the Lyapunov stability theory,the upper bound of convergence time which has nothing to do with the initial state is obtained,and the effectiveness of the control method is proved.(2)The fixed-time consensus problem of second-order nonlinear multi-agent systems under directed topology is studied.Design the control algorithm consists of distributed observer and observer-based decentralized controller to solve problem of nonlinear dynamics and achieve fixed-time consensus.According to the Lyapunov stability theory,it is proved that the distributed fixed-time observer can estimate the leader's state based on the directed topology,and the upper bound of observer's convergence time is obtained.Based on the homogeneous theory,the designed fixed-time controller does not have linear terms of errors,which can suppress nonlinear dynamics and make the followers track the leader.(3)The fixed-time connectivity-preserving consensus problem for second-order multi-agent systems with limited communication range is investigated.For the leaderless multi-agent systems,combined with the global sliding-mode control method,the fixed-time connectivity-preserving consensus protocol is designed.By constructing the energy function,the sufficient condition of maintaining initial communication topology is obtained.Based on the Lyapunov stability theory and the homogeneous theory,it is proved that the designed consensus protocol can overcome the external disturbances and make all agents reach an agreement on a common state within a fixed time.In addition,the results have also been extended to the multi-agent systems with a leader,achieving fixed-time connectivity-preserving consensus.