Robust and/or Adaptive Neural Networks for Dynamic System Identification

0114619 Lo在美国国家科学基金会资助的一个前期项目中，已经建立了具有长期和短期记忆（LASTM）的神经网络（NN）和风险敏感神经网络（NN）分别用于动态系统的自适应和鲁棒辨识的数学证明和数值可行性。 同样重要的是，已经发现了一种训练NN的自适应方法，该方法能够选择最适合于训练数据的训练标准，并避免所选训练标准的局部极小值。 新项目的目标是进一步发展这些想法和方法，进行彻底的基准研究，并开发更强大的算法，以完成建立这种神经计算方法来实现动态系统的鲁棒和/或自适应识别。主要任务包括：（1）在存在多重共线性的情况下，开发用于调整具有LASTM的NN的线性权重的在线递归算法，（2）将自适应风险搜索训练方法与使用来自统计学的鲁棒估计准则的现有方法进行比较;（3）开发了一种交替使用风险寻求和风险规避准则的算法，用于识别具有精细特征或欠精细特征的动态系统。（4）发展了一个理论的收敛特性的自适应风险规避训练方法的设想在前面的项目;（5）将上述自适应和鲁棒系统辨识思想相结合，对不确定环境下的动态系统进行辨识。

0114619LoIn a preceding project supported by NSF, mathematical justification and numerical feasibility of neural networks (NNs) with long- and short-term memories (LASTMs) and risk-sensitive NNs have been established for adaptive and robust identification of dynamic systems respectively. Equally important, an adaptive method of training NNs that has the ability to select a training criterion most suitable for the training data and to avoid poor local minima of the selected training criterion has been discovered. The objective of the new project is to further develop these ideas and methodologies, conduct thorough benchmarking studies, and develop more powerful algorithms in order to complete establishing this neurocomputing approach to robust and/or adaptive identification of dynamic systems.Among the key tasks are: (1) development of an online recursive algorithm for adjusting linear weights of an NN with LASTMs in the presence of multicollinearity, using possibly a combination of the Kalman filter and ridge regression; (2) comparison of adaptive risk-seeking training method against existing methods using robust estimation criteria from statistics; (3) development of an algorithm using risk-seeking and risk-averting criteria alternately in identifying a dynamic system with a fine feature or an under-represented segment in the presence of outlying measurement noises; (4) development of a theory of the convergence properties of the adaptive risk-averting training method conceived in the preceding project; (5) combination of the above adaptive and robust system identification ideas for identification of a dynamic system in an uncertain environment.