Nonlinear System Identification: A Wavelet based State Dependent Parameter Modeling Approach

The work documented in this book presents a new, efficient and systematic approach to the identification of nonlinear dynamic systems using Wavelet based State Dependent Parameter (SDP) models, from structure determination to parameter estimation. In this approach, the system's nonlinearities are analyzed and effectively represented by a SDP model structure in the form of wavelets. This provides a computationally efficient tool to open up the `black-box', offering valuable insights into the system's dynamics. Here, 1- dimensional (1-D) approach is first developed based on a conventional SDP model structure which relies on a single state variable dependency. It is then extended into a multi-dimensional approach in order to solve the identification problem of systems with significant multi-variable dependence nonlinear dynamics. The research as well investigates the aspects of noise, stability and other engineering application of the proposed approaches, including: nonlinear identification in the presence of noise, BIBO stability analysis and application studies where the developed approaches have been used in various engineering applications.