Finite Time Consistency And Formation Control For Multi-agent Systems

With the continuous development of automation,information and other disciplines,the collaborative control of multi-agent system is more and more widely used in practical applications.The research on consistency is the key to collaborative control in recent years and has become a hot topic in the field of control.In this paper,linear system theory,graph theory,matrix theory,Lyapunov stability as the main research tools,the consistency of nonlinear multi-agent system is studied as follows:1)The consistency problem of fixed time is proposed for the leader and follower multi-formation multi-agent system with nonlinear internal dynamics.Assuming that the total information received is zero by each team,a multi-formation control protocol based on neighborhood is proposed.Secondly,the stability of multi-agent system independent of initial conditions is obtained by using Lyapunov fixed time stability theorem.The consistency condition of switching topology structure is solved by using the fixed topology theorem.Finally,two numerical examples are given to illustrate the effectiveness of the proposed method.2)A consistency problem is proposed for a second-order multi-agent system with nonlinear dynamics and leaderless.Firstly,an adaptive control protocol is designed for a leaderless multi-agent system in a directed communication topology based on the position and speed of adjacent agents.Secondly,the nonlinear term of the system is solved by using quadratic bounded and one-sided Lipschitz condition.The sufficient conditions for nonlinear second-order leaderless multi-agent systems based on linear matrix inequality(LMI)form are obtained by using Lyapunov stability theorem,Kronecker product and Schur lemma.Finally,the validity of the theoretical analysis is verified by a simulation example.3)The fixed-time consistency problem is proposed for the second-order nonlinear multi-agent system.Firstly,a distributed adaptive control protocol is designed by using non-singular terminal sliding mode control.Secondly,the radial basis function neural network is used to process the nonlinear terms of the multi-agent system,and adaptive control is used to estimate the uncertain parameters.The error of multi-agent system was stabilized in fixed time by using Lyapunov stability theorem and graph theory.Finally,a simulation example is given to verify the effectiveness of the proposed control method.