Identification of nonlinear dynamical system using hierarchical clustering analysis and local linear models

This paper discusses the use of unsupervised learning and localized modeling to identify nonlinear dynamical systems from empirical series data. A finite-order nonlinear autoregressive (AR) model is constructed to capture the system dynamics. The embedded input space for the nonlinear AR model is partitioned into overlapped regions that are fine enough so that localized modeling techniques, such as local linear modeling, can approximate system dynamics well in each region. Subsequently, unsupervised learning, such as hierarchical clustering analysis, is used for partitioning the embedded input space to achieve the tradeoff between the model complexity and the approximation error. The performance of the proposed approach is evaluated on two numerical examples: (i) time series prediction; (ii) identification of SISO system. Simulation results demonstrate that the proposed approach can capture the nonlinear system dynamics well.