In 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.
