Delay Consensus Margin Of Low-Order Multi-Agent Systems

Multi-agent systems have received considerable attention in control fields due to their broad application in science and engineering.The consensus problem is the foundation of cooperation and coordination of multi-agent systems which amounts to designing a suitable feedback control protocol so that all the agents in a network converge to a common state.By its intrinsic nature the agents in a MAS configuration exchange information over a communication network,which is prone to transmission delays,it's of great significance to study the delay consensus margin problem of multi-agent systems with communication delay.In this thesis,the consensus protocols with communication delay are designed,and furthermore,the explicit delay consensus margin and both the upper bounds and lower bounds are given.The main contents are as follows:?For the first-order multi-agent systems with unstable poles,a P and PD consensus protocols with communication delay are designed.Based on the Routh stability criterion,the stability region of consensus controller parameters which ensure the first-order MAS achieve consensus under protocols without communication delay is obtained.The delay consensus margin of the first-order MAS under consensus protocols with communication delay is solved by the amplitude and phase angle matching method in the frequency domain.Furthermore,the upper bounds and lower bounds are obtained.?For the second-order multi-agent systems with unstable poles,the unstable poles of second-order gents are discussed in detail and divided into following four cases:(1)two unstable real poles;(2)two unstable complex conjugate poles;(3)a pair of oscillatory poles;(4)double integrators.The stability region of consensus controller parameters which ensure the second-order MAS achieve consensus under protocols without communication delay is obtained based on Routh stability criterion.When considering the communication delay,the maximum time delay which the second-order MAS can tolerate is obtained and the delay consensus margin is solved with the upper bounds and lower bounds.?Considering the containment problems of multi-agent systems with the structure of leader-follower,for the case of second-order MAS with two unstable real poles,the containment controller with communication delay of second-order MAS is designed.The delay consensus margin of the second-order MAS achieve containment is solved and furthermore,the explicit bounds of the delay consensus margin are obtained.