Consensus in directed networks of multiple agents, as an important topic, has become an active research subject. Over the past several years, some types of consensus problems have been studied. In this paper, we propo...Consensus in directed networks of multiple agents, as an important topic, has become an active research subject. Over the past several years, some types of consensus problems have been studied. In this paper, we propose a novel type of consensus, the generalized consensus （GC）, which includes the traditional consensus, the anti-consensus, and the cluster consensus as its special cases. Based on the Lyapunov＇s direct method and the graph theory, a simple control algorithm is designed to achieve the generalized consensus in a network of agents. Numerical simulations of linear and nonlinear GC are used to verify the effectiveness of the theoretical analysis.展开更多
In this paper, we give a comment on the dislocated-neighbourhood systems due to Hitzler and Seda [1]. Also, we recover the open sets of the dislocated topology.
Based on the theory of products of generalized topologies,we introduce the product mappings and the diagonal mappings in generalized topological spaces in this paper.We investigate some basic properties(especially,the...Based on the theory of products of generalized topologies,we introduce the product mappings and the diagonal mappings in generalized topological spaces in this paper.We investigate some basic properties(especially,the continuity,openness and closedness)of the product mappings and the diagonal mappings in generalized topological spaces.Some applications are given to answer two questions raised in[3].展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11002061 and 11202084)the Fundamental Research Funds for the Central Universities,China(Grant No.JUSRP51317B)
文摘Consensus in directed networks of multiple agents, as an important topic, has become an active research subject. Over the past several years, some types of consensus problems have been studied. In this paper, we propose a novel type of consensus, the generalized consensus （GC）, which includes the traditional consensus, the anti-consensus, and the cluster consensus as its special cases. Based on the Lyapunov＇s direct method and the graph theory, a simple control algorithm is designed to achieve the generalized consensus in a network of agents. Numerical simulations of linear and nonlinear GC are used to verify the effectiveness of the theoretical analysis.
文摘In this paper, we give a comment on the dislocated-neighbourhood systems due to Hitzler and Seda [1]. Also, we recover the open sets of the dislocated topology.
基金Supported by the National Natural Science Foundation of China(11501404)Jiangsu Planned Talent Projects(2016-JY-078)+1 种基金Jiangsu Jiaogai Projects Fundations(2017JSJG490)Jiangsu Qing Lan Project(PY2016006)。
文摘Based on the theory of products of generalized topologies,we introduce the product mappings and the diagonal mappings in generalized topological spaces in this paper.We investigate some basic properties(especially,the continuity,openness and closedness)of the product mappings and the diagonal mappings in generalized topological spaces.Some applications are given to answer two questions raised in[3].
