Research On Consensus Control Of Linear Continuous-Time Third-Order Multi-Agent Systems

In recent years,the cooperative control of multi-agent systems has attracted more and more attention of researchers.Different from traditional centralized control,the distributed cooperative control has better robustness,flexibility,and adaptability.It is widely adopted in military,agriculture,and transportation fields.The consensus problem is fundamental in the research of multi-agent system cooperative control.The main task of multi-agent consensus is to design a suitable control algorithm according to the communication topology of the system,so that the states of all individuals in the system can finally reach a consistent state.For example,the position and speed of the robot formation are consistent,and the attitude of the satellite group is consistent,etc.In actual engineering,many high-order multi-agent systems have complex dynamic structures,and simple first-order or second-order models cannot describe their internal characteristics well.Therefore,this thesis mainly addresses the problems related to the consensus of linear continuous-time third-order multi-agent systems.The influence of communication delay and the group control of agents are also studied.The structure of the thesis is organized as follows:First,the research background and the research status of multi-agent consensus are explained in detail.Some related preliminary knowledge such as graph theory and matrix theory are also introduced.Second,the consensus problem of the third-order multi-agent system without delay is studied.The original system is transformed into an error system with the consensus control protocol.The stability analysis of the system is performed by the use of graph theory,matrix theory,and Routh-Hurwitz stability criterion.The necessary and sufficient conditions for the system to achieve asymptotic consensus under an undirected topology are presented.Numerical simulations verify the effectiveness of the designed algorithm.Third,the consensus problem of the third-order multi-agent system with communication delay is studied.For the case where the system's topology contains a directed spanning tree,Generalized Nyquist criterion and Gerschgorin's disc theorem are used to derive sufficient conditions for the system to converge.The explicit calculation formula of the maximum communication delay with which the system can tolerate is obtained.For the case where the system's topology is an undirected graph,an effective control algorithm is also given.The correctness of the conclusion is verified by numerical simulations.Finally,the group consensus problem of the third-order multi-agent system is studied and suitable group control protocols are designed for multi-agent models.The stability analysis of the system is completed by the use of Matrix theory and Routh-Hurwitz stability criterion.In the two cases where the system topology is a connected graph and an undirected graph,the relevant sufficient conditions for the system to reach asymptotic consensus are drawn,respectively.Numerical simulations show that the stability of the system is determined by the coupling strength parameters and the non-zero eigenvalues of the system's Laplacian matrix.