Average Consensus Of Multi-Agents With Time-Delay And Controlled By PD Algorithm

The average consensus of multi-agent systems is a fundamental and important problem in the field of control,and has a wide application in related engineering.Thus,the average consensus of multi-agent systems with time delay is investigated in this thesis.A PD algorithm is introduced to study the influence of the parameters on the consensus.By looking for the combination of parameters which corresponds the shortest transient time for this system,the thesis specifies the proportional parameter is y=1.0,and combine time delay ? and differential parameter ?arbitrarily by simulation.the optimal values of the proportional parameter and differential parameter are respectively ?=0.91 and ?=0.26 when the value of time delay ? is less than or equal to 0.48.Under the optimal parameter,the balanced of average consensus problem in fixed topology&strong connected systems is studied.As time delay is ??0.48,the proportional and differential parameters will be the same as preceding by using PD Algorithm.The thesis founds that the number of agents n in the system is power-dependent with its algebraic connectivity A,A?n?(?<0),and power-corresponding to its average consensus time T,T? n?(?>0)by simulation and analyses.This conclusion can predict average consensus time in directed network systems that transmits information sequentially.The average consensus of multi-agent systems with time delay in switched topology is studied.The thesis uses the Lyapunov-Krasovskii function to prove the system stability,and verified its correctness by MATLAB.The thesis found that when four balanced strong connected in 10 agents systems with delay are added to an edge,its algebraic connectivity and average consensus time are all equal.When the information communication channel is blocked in the directed fixed topology,the conclusion makes all agents realize the information by switched topology.