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针对信息交流会因某些因素导致通信时延的发生,研究了具有通信时延的多个体系统受限一致性问题。假定每个个体具有一阶连续动力学行为,并设计一个带有通信时延的控制协议。但其个体状态受限于一个凸交集,且多个体系统构成的无向网络拓扑是动态切换的。在通信时延固定且有界的前提下,一方面提出的一致性协议可使每个个体的状态最终达成一致,设计合适的Lyapunov-Krasovskii函数可以证明这一结论;另一方面,利用投影算法,将个体状态不在凸集的所有个体投影在某一个凸集(受限集)内,目的是使多个体系统最终的一致性值位于所有个体状态凸受限集的交集。综合以上两方面,就实现了在通信时延情形下的多个体系统受限一致性。
Aiming at the communication delay caused by some factors in the exchange of information, the restricted consistency of multiple systems with communication delay is studied. It is assumed that each individual has first-order continuous dynamic behavior and designs a control protocol with communication delay. But its individual state is limited by a convex intersection, and the multi-body system composed of undirected network topology is dynamically switched. On the premise of a fixed and bounded communication delay, the consistency protocol proposed on the one hand can finally achieve the agreement of each individual’s state. Proper Lyapunov-Krasovskii function can prove this conclusion. On the other hand, , All individuals whose state is not in convex set are projected onto a convex set (restricted set) in order to make the final consistency value of multiple systems lie in the intersection of convex sets of all individual states. The above two aspects combine to realize the limited consistency of multiple systems in the case of communication delay.