Research On Lag Consensus Of Multi-agent Systems

Multi-agent systems have been comprehensively applied in drone search,air traffic control,satellite formation flight,program of automated highway system and distributed majorization of multiagent robot systems.Thence,multiagent systems based on coordinated control have attracted great concentration from the scientific community in nowadays,and have gradually become an increasingly mature up-and-coming control method in the control field.This is mainly due to the distributed,interactivity,autonomy and so on,which fits the features of the systems such as complexity,dynamics and openness.Consensus,as the basic problem of the primary research,refers to the interaction among neighboring agents with the appropriate control protocol to insure the state of all agents converge.However,in practical engineering applications,the controlled system which is considered in this paper is often complex,uncertain and nonlinear,and is usually influenced by communication delays and control parameters.It is extremely tough to achieve precise control in the system model,which is result to unable to achieve sufficient conditions for consensus.Thence,this paper aims to study the lag consensus of multi-agent systems in order to solve the problem that traditional consensus cannot be achieved and in order to better reflect the interactivity and collaboration of the system.As an extension of consensus research,lag consensus has also attracted great concentration from the scientific community in nowadays.The meaning of lag consensus is that multiple agents of a multi-agent system reach the same state within a given lag time.Compared with traditional consensus,lag consensus can reflect the performance of information transmission between individuals more better.When the lag time is zero,the degradation process from lag consensus to traditional consensus has been realized.In real life,there exists a phenomenon that the sequence reaches the same order everywhere.For example,the well-aligned passage of transportation on the road and the well-aligned parking of transportation in the parking lot all reflect the characteristics of lag consensus.Therefore,the research of lag consensus has incredible values.1.Firstly,based on graph theory,a complex and changeable discrete linear leader-follower system model with real-time communication has been given.Secondly,the public Lyapunov functional differential equation is selected,and a constraint condition and corresponding proof for the existence of lag consensus in the system without communication delay are given.Based on the above research,an improvement is realized on the basis of the original system model,and a communication delay is introduced into the control protocol,which leads to the system realizing the lag consensus condition.At last,the feasibility of the results of model has been verified by contrasting the simulation results.2.Considering the constraint condition of lag consensus is satisfied in the discrete state,there are nonlinear dynamic factors in the follower system model,so the processing of nonlinear terms have become the key point of the research.First,a second-order discrete nonlinear multi-agent system model is built up,and the error system of the model is obtained.Thence,the lag is brought in to satisfy the stability of LMI and the analysis is achieved in accordance with the fabric of the Lyapunov function to prove that the stability condition is reasonable.Finally,the stability is applied to full fill the sufficient condition for the lag consensus of system.3.Consider the multi-agent system model with time-varying delay as well as Markov switching topology under the action of adaptive control and pinning control.In the systems considered above,there must be a directed path between individuals,which will cause troubles such as information blockage during the transmission process.It is the reason that why introduce pinning control.Moreover,for the sake of optimizing the system capability,introducing the adaptive control effectively decreases the restrained parameters and increases the stability of the systems.Using the Lyapunov function and the infinitesimal operator algorithm,the system with time-varying time-delay and Markov switching topology realizes the sufficient conditions and corresponding proofs for lag consensus.