Robust and/or Adaptive Neural Networks for Dynamic System Identification

0114619Lo 在 NSF 支持的先前项目中，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的数学论证和数值可行性，分别用于动态系统的自适应和鲁棒识别。 同样重要的是，已经发现了一种训练神经网络的自适应方法，该方法能够选择最适合训练数据的训练标准，并避免所选训练标准的不良局部最小值。 新项目的目标是进一步发展这些想法和方法，进行彻底的基准测试研究，并开发更强大的算法，以完成建立这种鲁棒和/或自适应动态系统识别的神经计算方法。关键任务包括：（1）开发在线递归算法，用于在存在多重共线性的情况下调整带有 LASTM 的神经网络的线性权重，可能使用卡尔曼滤波器和岭回归的组合； (2) 使用统计中的稳健估计标准，将自适应风险寻求训练方法与现有方法进行比较； (3) 开发一种算法，交替使用风险寻求和风险规避标准，以识别具有精细特征的动态系统或在存在外围测量噪声的情况下识别代表性不足的部分； (4) 发展先前项目中设想的自适应风险规避训练方法的收敛特性理论； (5)结合上述自适应和鲁棒系统辨识思想，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.