Local dynamic modeling with self-organizing maps and applications to nonlinear system identification and control

The technique of local linear models is appealing for modeling complex time series due to the weak assumptions required and its intrinsic simplicity. Here, instead of deriving the local models from the data, we propose to estimate them directly from the weights of a self-organizing map (SOM), which functions as a dynamic preserving model of the dynamics. We introduce one modification to the Kohonen learning to ensure good representation of the dynamics and use weighted least squares to ensure continuity among the local models. The proposed scheme is tested using synthetic chaotic time series and real-world data. The practicality of the method is illustrated in the identification and control of the NASA Langley wind tunnel during aerodynamic tests of model aircraft. Modeling the dynamics with an SOM lends to a predictive multiple model control strategy. Comparison of the new controller against the existing controller in test runs shows the superiority of our method.