Research Of Consensus Protocols Based On The Variant D-path Laplacian For Multi-agent Systems

At present,the research on cooperation control of multi-agent systems(MASs)has attracted the interest of scientists in many fields such as traffic control,formation flying,robotic sensor networks,automated web navigation,etc.In general,collaborative control of multi-agent systems achieves common goals through information interactions between each agent and its nearest neighbor individuals.However,several studies have shown that each agent can not only communicate with individual neighbors,but also communicate with indirect neighbors through multi-step information interaction.Therefore,this paper will provide an in-depth study of multi-agent consensus under multistep information interaction,and provide mathematical models and analytical methods for network harmonic oscillators systems and linear parameter varying(LPV)systems.The specific work are as follows:(1)A variant-path Laplacian is first defined to describe the multi-step information interaction in directed graphs.As an extension of the general Laplacian,the new concept simplifies the acquirement of the d-path Laplacian by using the adjacency matrix to replace the irreducible shortest paths.Further,in the variant d-path Laplacian matrix associated with an unweighted directed graph,for two agents with multiple different shortest paths and these shortest paths having the same length,the corresponding element in the variant d-path Laplacian matrix is the number of the shortest paths.So this way of the definition in the variant d-path Laplacian matrix is more suitable in the social networks.(2)A consensus protocol based on directed graphs with the variant d-path Laplacian is designed for network harmonic oscillator systems from the perspective of output information.It is demonstrated through theoretical analysis that the network harmonic oscillator systems without time delay eventually achieves consensus when the directed graph contains a spanning tree and systems satisfy sufficient coupling strength conditions.while for networked harmonic oscillators with time delay,the upper bound condition of the time delay is further analyzed to obtain,and it is shown that the system can achieve consensus under sufficient coupling strength conditions and bounded time delays.(3)The criterion for achieving robust consensus in multi-agent systems is proved theoretically in the presence of linear parameter variations.For multiple agents interplay on an undirected graph,the problem of distributed negotiation protocol and adaptive protocol design of the system is first addressed to achieve robust consensus.Secondly,the concept of d-path Laplacian is introduced to investigate the feasibility of linear parameter varying multi agent systems controlled by the adaptive strategy to communicate on the directed graph,and analyze the sufficient conditions to achieve robust consensus,in order for the elimination of the dependence on the topology information.