The properties of generalized flip Markov chains on connected regular digraphs are discussed.The 1-Flipper operation on Markov chains for undirected graphs is generalized to that for multi-digraphs.The generalized 1-F...The properties of generalized flip Markov chains on connected regular digraphs are discussed.The 1-Flipper operation on Markov chains for undirected graphs is generalized to that for multi-digraphs.The generalized 1-Flipper operation preserves the regularity and weak connectivity of multi-digraphs.The generalized 1-Flipper operation is proved to be symmetric.Moreover,it is presented that a series of random generalized 1-Flipper operations eventually lead to a uniform probability distribution over all connected d-regular multi-digraphs without loops.展开更多
Communication bandwidth and network topology are two important factors that affect performance of distributed consensus in multi-agent systems.The available works about quantized average consensus assume that the adja...Communication bandwidth and network topology are two important factors that affect performance of distributed consensus in multi-agent systems.The available works about quantized average consensus assume that the adjacency matrices associated with the digraphs are doubly stochastic,which amounts to that the digital networks are balanced.However,this assumption may be unrealistic in practice.In this paper,without assuming double stochasticity,the authors revisit an existing quantized average consensus protocol with the logarithmic quantization scheme,and investigate the quantized consensus problem in general directed digital networks that are strongly connected but not necessarily balanced.The authors first derive an achievable upper bound of the quantization precision parameter to design suitable logarithmic quantizer,and this bound explicitly depends on network topology.Subsequently,by means of the matrix transformation and the Lyapunov techniques,the authors provide a testable condition under which the weighted average consensus can be achieved with the proposed quantized protocol.展开更多
基金National Natural Science Foundation of China(No.11671258)。
文摘The properties of generalized flip Markov chains on connected regular digraphs are discussed.The 1-Flipper operation on Markov chains for undirected graphs is generalized to that for multi-digraphs.The generalized 1-Flipper operation preserves the regularity and weak connectivity of multi-digraphs.The generalized 1-Flipper operation is proved to be symmetric.Moreover,it is presented that a series of random generalized 1-Flipper operations eventually lead to a uniform probability distribution over all connected d-regular multi-digraphs without loops.
基金Supported by National Natural Science Foundation of China （61273108）, the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, the Fundamental Research Funds for the Central Universities （106112013CD- JZR175501）
基金supported by the National Natural Science Foundation of China under Grant No.60904064, 61174094the Program for New Century Excellent Talents in University of China(NCET-10-0506)the Tianjin Natural Science Foundation of China under Grant No.09JCYBJC01700
基金supported by the Major State Basic Research Development Program of China(973 Program)under Grant No.2010CB731400the Natural Science Foundation of China under Grant Nos.61074125,61073102,61170059,61170172,61272153Anhui Provincial Natural Science Foundation under Grant No.090412251
文摘Communication bandwidth and network topology are two important factors that affect performance of distributed consensus in multi-agent systems.The available works about quantized average consensus assume that the adjacency matrices associated with the digraphs are doubly stochastic,which amounts to that the digital networks are balanced.However,this assumption may be unrealistic in practice.In this paper,without assuming double stochasticity,the authors revisit an existing quantized average consensus protocol with the logarithmic quantization scheme,and investigate the quantized consensus problem in general directed digital networks that are strongly connected but not necessarily balanced.The authors first derive an achievable upper bound of the quantization precision parameter to design suitable logarithmic quantizer,and this bound explicitly depends on network topology.Subsequently,by means of the matrix transformation and the Lyapunov techniques,the authors provide a testable condition under which the weighted average consensus can be achieved with the proposed quantized protocol.
