In this paper,we presented the decentralized supervisory control problem of discrete event system with continuous-time variable.By presenting the definition of coobservability for the timed specification,a necessary and sufficient condition for the existence of decentralized supervisors is obtained.Finally,a numerical example is given.
Fei WANG,Fu-jiang JIN,Ji-liang LUO (College of Information Science and Engineering,Huaqiao University,Xiamen,Fujian,361021,P.R.China)
For accelerating the supervised learning by the SpikeProp algorithm with the temporal coding paradigm in spiking neural networks (SNNs), three learning rate adaptation methods (heuristic rule, delta-delta rule, and delta-bar-delta rule), which are used to speed up training in artificial neural networks, are used to develop the training algorithms for feedforward SNN. The performance of these algorithms is investigated by four experiments: classical XOR (exclusive or) problem, Iris dataset, fault diagnosis in the Tennessee Eastman process, and Poisson trains of discrete spikes. The results demonstrate that all the three learning rate adaptation methods are able to speed up convergence of SNN compared with the original SpikeProp algorithm. Furthermore, if the adaptive learning rate is used in combination with the momentum term, the two modifications will balance each other in a beneficial way to accomplish rapid and steady convergence. In the three learning rate adaptation methods, delta-bar-delta rule performs the best. The delta-bar-delta method with momentum has the fastest convergence rate, the greatest stability of training process, and the maximum accuracy of network learning. The proposed algorithms in this paper are simple and efficient, and consequently valuable for practical applications of SNN.
