The discrete-time first-order multi-agent networks with communication noises are under consideration. Based on the noisy observations, the consensus control is given for networks with both fixed and time-varying topol...The discrete-time first-order multi-agent networks with communication noises are under consideration. Based on the noisy observations, the consensus control is given for networks with both fixed and time-varying topologies. The states of agents in the resulting closed-loop network are updated by a stochastic approximation （SA） algorithm, and the consensus analysis for networks turns to be the convergence analysis for SA. For networks with fixed topologies, the proposed consensus control leads to consensus of agents with probability one if the graph associated with the network is connected. In the case of time-varying topologies, the similar results are derived if the graph is jointly connected in a fixed time period. Compared with existing results, the networks considered here are in a more general setting under weaker assumptions and the strong consensus is established by a simpler proof.展开更多
This paper considers the convergence rate of an asymmetric Deffuant-Weisbuch model.The model is composed by finite n interacting agents.In this model,agent i’s opinion is updated at each time,by first selecting one r...This paper considers the convergence rate of an asymmetric Deffuant-Weisbuch model.The model is composed by finite n interacting agents.In this model,agent i’s opinion is updated at each time,by first selecting one randomly from n agents,and then combining the selected agent j’s opinion if the distance between j’s opinion and i’s opinion is not larger than the confidence radiusε0.This yields the endogenously changing inter-agent topologies.Based on the previous result that all agents opinions will converge almost surely for any initial states,the authors prove that the expected potential function of the convergence rate is upper bounded by a negative exponential function of time t when opinions reach consensus finally and is upper bounded by a negative power function of time t when opinions converge to several different limits.展开更多
The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures.This paper includes eight sections.Section 1 is a longer introductio...The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures.This paper includes eight sections.Section 1 is a longer introduction,which gives a brief introduction to random metric theory,risk measures and conditional risk measures.Section 2 gives the central framework in random metric theory,topological structures,important examples,the notions of a random conjugate space and the Hahn-Banach theorems for random linear functionals.Section 3 gives several important representation theorems for random conjugate spaces.Section 4 gives characterizations for a complete random normed module to be random reflexive.Section 5 gives hyperplane separation theorems currently available in random locally convex modules.Section 6 gives the theory of random duality with respect to the locally L0-convex topology and in particular a characterization for a locally L0-convex module to be L0-pre-barreled.Section 7 gives some basic results on L0-convex analysis together with some applications to conditional risk measures.Finally,Section 8 is devoted to extensions of conditional convex risk measures,which shows that every representable L∞-type of conditional convex risk measure and every continuous Lp-type of convex conditional risk measure(1 ≤ p < +∞) can be extended to an L∞F(E)-type of σ,λ(L∞F(E),L1F(E))-lower semicontinuous conditional convex risk measure and an LpF(E)-type of T,λ-continuous conditional convex risk measure(1 ≤ p < +∞),respectively.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.60774020, 60821091,and 60874001
文摘The discrete-time first-order multi-agent networks with communication noises are under consideration. Based on the noisy observations, the consensus control is given for networks with both fixed and time-varying topologies. The states of agents in the resulting closed-loop network are updated by a stochastic approximation （SA） algorithm, and the consensus analysis for networks turns to be the convergence analysis for SA. For networks with fixed topologies, the proposed consensus control leads to consensus of agents with probability one if the graph associated with the network is connected. In the case of time-varying topologies, the similar results are derived if the graph is jointly connected in a fixed time period. Compared with existing results, the networks considered here are in a more general setting under weaker assumptions and the strong consensus is established by a simpler proof.
基金supported by the Young Scholars Development Fund of Southwest Petroleum University(SWPU)under Grant No.201499010050the Scientific Research Starting Project of SWPU under Grant No.2014QHZ032+1 种基金the National Natural Science Foundation of China under Grant No.61203141the National Key Basic Research Program of China(973 Program)under Grant No.2014CB845301/2/3
文摘This paper considers the convergence rate of an asymmetric Deffuant-Weisbuch model.The model is composed by finite n interacting agents.In this model,agent i’s opinion is updated at each time,by first selecting one randomly from n agents,and then combining the selected agent j’s opinion if the distance between j’s opinion and i’s opinion is not larger than the confidence radiusε0.This yields the endogenously changing inter-agent topologies.Based on the previous result that all agents opinions will converge almost surely for any initial states,the authors prove that the expected potential function of the convergence rate is upper bounded by a negative exponential function of time t when opinions reach consensus finally and is upper bounded by a negative power function of time t when opinions converge to several different limits.
基金supported by National Natural Science Foundation of China (Grant No.10871016)
文摘The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures.This paper includes eight sections.Section 1 is a longer introduction,which gives a brief introduction to random metric theory,risk measures and conditional risk measures.Section 2 gives the central framework in random metric theory,topological structures,important examples,the notions of a random conjugate space and the Hahn-Banach theorems for random linear functionals.Section 3 gives several important representation theorems for random conjugate spaces.Section 4 gives characterizations for a complete random normed module to be random reflexive.Section 5 gives hyperplane separation theorems currently available in random locally convex modules.Section 6 gives the theory of random duality with respect to the locally L0-convex topology and in particular a characterization for a locally L0-convex module to be L0-pre-barreled.Section 7 gives some basic results on L0-convex analysis together with some applications to conditional risk measures.Finally,Section 8 is devoted to extensions of conditional convex risk measures,which shows that every representable L∞-type of conditional convex risk measure and every continuous Lp-type of convex conditional risk measure(1 ≤ p < +∞) can be extended to an L∞F(E)-type of σ,λ(L∞F(E),L1F(E))-lower semicontinuous conditional convex risk measure and an LpF(E)-type of T,λ-continuous conditional convex risk measure(1 ≤ p < +∞),respectively.
