Research On The Distributed Consensus Of Multi-agent Systems With Time Delay

In recent years,with the widespread application of distributed control of multi-agent systems in the formation control of UAVs,the cooperative control of mobile robots,the state estimation,researchers in many fields at home and abroad have generated a strong research interest.The distributed consensus problem has become an important and classic subject in the field of control science,and it is also the basis of the distributed coordinated control problem.In the field of actual engineering technology,due to the influence of various factors,such as limited communication resources and the time required for data processing and calculation,the system will inevitably have a time delay.The existence of time delay will increase the complexity of the system studied,so that the original control protocol will no longer be applicable when the system achieves consensus,and a new protocol needs to be redesigned.The time delay in this paper is mainly the input time delay and the communication time delay,both of which are time-varying.Therefore,the study of distributed consensus of time-delayed systems has a high theoretical value,and also has great guiding significance for practical engineering applications.Based on previous studies,this paper studies the consensus problem based on the necessary analysis tools such as algebraic graph theory,Lyapunov stability theory,linear matrix inequality,schur complement theorem and related lemmas,and gives some assumptions to meet sufficient conditions for the system to achieve consensus under these conditions.Moreover,a numerical simulation example based on MATLAB software verifies the effectiveness of the designed protocol.The main research contents are as follows:Firstly,for a stochastic nonlinear system containing a leader with time-varying communication delay and time-varying actuator failure,a new distributed consensus protocol is proposed,and sufficient conditions of the system consensus under directed topology is given.The introduction of stochastic nonlinear terms and time-varying communication delays makes the system dynamics model more universal and representative.Compared with previous control protocols,the new control protocol has a wider scope of application.Since the time delay existing in the system is not static and will also change with time,studying time-varying time delay is more theoretically valuable.Therefore,the research of the above types of systems is of great application value.Secondly,for a class of nonlinear systems with parameter uncertainties and time-varying input delays,a new distributed adaptive protocol is proposed,and sufficient conditions of consensus for system under undirected topology are given.For the processing method of nonlinear terms in the system,the difference from the past is to introduce the theorem of one-sided Lipschitz nonlinear conditions and quadratic internal bounded nonlinear conditions.Since the above theorem can be applied to a nonlinear system with a larger Lipschitz constant,the results of this study are less conservative and more general.Finally,for a class of nonlinear time-delay multi-agent systems with randomly disturbance,randomly parameter uncertainties,and randomly varying nonlinearities,a distributed nonlinear consensus protocol under switching topology is proposed,which is also obtained through a series of theoretical derivations to meet sufficient conditions for consensus.In this paper,two random variables that obey Bernoulli distribution are introduced,and their distribution laws are different.The future application of the nonlinear consensus protocol designed for nonlinear systems is also very large,and it has more theoretical research value.