A new type of recurrent neural network is discussed, which provides the potential for modelling unknown nonlinear systems. The proposed network is a generalization of the network described by Elman, which has three la...A new type of recurrent neural network is discussed, which provides the potential for modelling unknown nonlinear systems. The proposed network is a generalization of the network described by Elman, which has three layers including the input layer, the hidden layer and the output layer. The input layer is composed of two different groups of neurons, the group of external input neurons and the group of the internal context neurons. Since arbitrary connections can be allowed from the hidden layer to the context layer, the modified Elman network has more memory space to represent dynamic systems than the Elman network. In addition, it is proved that the proposed network with appropriate neurons in the context layer can approximate the trajectory of a given dynamical system for any fixed finite length of time. The dynamic backpropagation algorithm is used to estimate the weights of both the feedforward and feedback connections. The methods have been successfully applied to the modelling of nonlinear plants.展开更多
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 uses a finite dominating set （FDS） to investigate the multi-facility ordered median problem （OMP） in a strongly connected directed network. The authors first prove that the multi-facility OMP has an FDS...This paper uses a finite dominating set （FDS） to investigate the multi-facility ordered median problem （OMP） in a strongly connected directed network. The authors first prove that the multi-facility OMP has an FDS in the node set, which not only generalizes the FDS result provided by Kalcsics, et al. （2002）, but also extends the FDS result from the single-facility Case to the multiple case, filling an important gap. Then, based on this FDS result, the authors develop an exact algorithm to solve the problem. However, if the number of facilities is large, it is not practical to find the optimal solution, because the multi-facility OMP in directed networks is NP-hard. Hence, we present a constant-approximation algorithm for the p-median problem in directed networks. Finally, we pose an open problem for future research.展开更多
文摘A new type of recurrent neural network is discussed, which provides the potential for modelling unknown nonlinear systems. The proposed network is a generalization of the network described by Elman, which has three layers including the input layer, the hidden layer and the output layer. The input layer is composed of two different groups of neurons, the group of external input neurons and the group of the internal context neurons. Since arbitrary connections can be allowed from the hidden layer to the context layer, the modified Elman network has more memory space to represent dynamic systems than the Elman network. In addition, it is proved that the proposed network with appropriate neurons in the context layer can approximate the trajectory of a given dynamical system for any fixed finite length of time. The dynamic backpropagation algorithm is used to estimate the weights of both the feedforward and feedback connections. The methods have been successfully applied to the modelling of nonlinear plants.
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This research is supported by the National Natural Science Foundation of China under Grant No. 70901050 and Macao Foundation under Grant No. 0144.
文摘This paper uses a finite dominating set （FDS） to investigate the multi-facility ordered median problem （OMP） in a strongly connected directed network. The authors first prove that the multi-facility OMP has an FDS in the node set, which not only generalizes the FDS result provided by Kalcsics, et al. （2002）, but also extends the FDS result from the single-facility Case to the multiple case, filling an important gap. Then, based on this FDS result, the authors develop an exact algorithm to solve the problem. However, if the number of facilities is large, it is not practical to find the optimal solution, because the multi-facility OMP in directed networks is NP-hard. Hence, we present a constant-approximation algorithm for the p-median problem in directed networks. Finally, we pose an open problem for future research.
