Research On Security Consensus And Algorithm For Delayed Discrete-time Multi-agent Systems

The distributed coordinated control of multi-agent systems has been widely applieded in many complex systems,such as intelligent transportation,intelligent power grid,flight formation and so on due to its advantages of strong robustness,great error tolerance,and low energy consumption.As a basic problem in coordinated control of complex systems,consensus problem means the status of all individuals in the system becomes convergent only by communcating with each other locally without central control within a certain time.However,in addition to being affected by time delays and various types of noise data,complex systems also face problems with their own individual parameter errors and equipment failures,and may even encounter external malicious attacks,the security of complex systems has gradually attracted widespread attention from domestic and foreign researchers in rencent years.Therefore,the research on the problem of secure coordinate control of conplex systems is particularly important.Based on the existing research work,the security consensus of two types of multi-agent systems under the influence of delay are discussed separately through the knowledge of probability theory,algebraic graph theory,matrix theory and stability theory in this thesis.The specific contents of this paper are as follows:For a class of discrete-time multi-agent systems with Byzantine malicious nodes,the safe consensus problem under the influence of time delay is studied.With a standard deviation of the expected distance as a constraint,a class of tolerant safe consensus algorithms is designed.The algorithm uses the neighbor time delay information sequence including its own information,and selects the effective optimal information as the control input with the constraints as the range,so that normal agents in the system can achieve safe consensus under certain conditions.By using graph theory,matrix theory,and stability theory of complex systems,the necessary and sufficient conditions for the system to achieve safe consensus are obtained.Finally,the simulation results verify the proposed safe consensus algorithm and the results of theoretiacl analysis.The results of simulations show that the algorithm not only enhances the system's resistance to malicious agents,but also reduces the topology connectivity requirements of mormal agents in the system.In addition,the experimental results also show that although thecommunication delay does not affect the realization of system security,but it will affect with the convergence speed of the system.Agents of complex systems do not only have cooperative or competitive relationships,but also have complex relationships of cooperation and competition at the same time.For a class of discrete-time multi-agent systems with communication delay,the problem of security group consensus is discussed.There is cooperative and competitive relationship between normal agents in the system,normal individuals could not only be attacked by external malicious nodes,but also compete with normal individuals in different groups.Based on the safe consensus algorithm,a type of safe consensus protocol under a cooperative-competitive relationship is designed,and using Gael's disk theorem,matrix theory and Nyquist stability theory and so on,the algebraic conditions for the system to achieve safe group consensus are given by analysis.Finally,the simulations verified the correctness of the theoretical results and the effectiveness of the designed protocol when peocessing in malicious node attacks and cooperative-competitive ralationships.Finally,the thesis' s work was summarized and the future work was prospected.