引用本文:冯芙叶,魏正红,刘付显.求解广义特征根问题的反馈神经网络方法[J].控制理论与应用,2006,23(4):645~648.[点击复制]
FENG Fu-ye, WEI Zheng-hong, LIU Fu-xian.Recurrent neural network for solving the generalized eigenvalue problem[J].Control Theory and Technology,2006,23(4):645~648.[点击复制]
求解广义特征根问题的反馈神经网络方法
Recurrent neural network for solving the generalized eigenvalue problem
摘要点击 1312  全文点击 796  投稿时间：2005-04-12  修订日期：2005-08-24
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DOI编号  10.7641/j.issn.1000-8152.2006.4.029
  2006,23(4):645-648
中文关键词  广义特征根问题  反馈神经网络  拟全局稳定性
英文关键词  generalized eigenvalue problem  recurrent neural network  global quasi-convergence
基金项目  
作者单位
冯芙叶,魏正红,刘付显 空军工程大学 导弹学院,陕西 三原710038
东莞理工学院 软件学院,广东 东莞523000
深圳大学 师范学院数学系,广东 深圳518060 
中文摘要
      研究了广义特征根问题求解的神经网络方法,给出了求解该问题的一个时间连续性反馈网络模型,利用LaSalle不变原理分析并证明了该网络的拟全局收敛性,这是网络能够确切的求解广义特征根问题的保证．同时,该网络解决了已有的基于罚函数方法构造的特征根问题的神经网络存在的一些基本缺陷:其一,基于罚函数的网络模型所得到的解可能不是真解,甚至可能都不是可行解;其二,它们的共同缺陷是有一个需要调节的参数,但是参数的选择并没有一个可供参考的准则;其三,这些模型的稳定性无法保证．本文所提出的网络模型解决了这些问题,并且,此网络具有一个很好的特征就是在初始点选定在问题的可行解集的话,网络轨线将永远是可行的并收敛到一个广义特征向量．最后,数值模拟也表明这里所提出的网络的可靠性能,进一步证明了此网络可以很好地求解广义特征根问题．
英文摘要
      Neural network method for solving generalized eigenvalue and eigenvector problems is studied in this paper and a continuous-time recurrent neural network model is presented. By using LaSalle's invariant principle, it is shown that the proposed network is globally quasi-convergent which guarantees an exact generalized eigenvector that can be found by the new model. Furthermore, this new model overcomes the following three defects in the existing neural network models based on penalty function method. 1) False solutions may be found by using penalty function method, sometimes, even unfeasible solutions could be found. 2) There is a parameter to be tuned in the process, but no definite rule available for the tuning. 3) No any stability result could be ensured for the existing models. The new model proposed here solves all these problems and, moreover, it has a good characteristic that it's trajectories can never escape from the feasible region, but will converge to the set of the generalized eigenvectors for any initial point in the feasible set. Finally, good performance of the proposed model for finding a generalized eigenvector is also demonstrated by numerical simulation results.