Study on Identification of Nonlinear Systems Using Quasi-ARX Models

System identification can be used to construct a model to represent a given system, and it plays an important role in system analysis, control and prediction. From the view of application, conventional nonlinear black-box models are not good since an easy-to-use model is to interpret properties of the nonlinear process, rather than treated as vehicles for adjusting the fit to the data. Therefore, some careful modeling is needed for certain applications, and prior knowledge from system is inspired to be combined with formal properties of the model. Quasi-linear autoregressive with exogenous inputs (quasi-ARX) modeling scheme provides an effective approach to extend well-studied and user-friendly linear techniques to nonlinear applications. It constructs models consisting of two parts: a macro-part and a core-part. The macro-part owns a useful interface to introduce some properties favorable to specific applications, and the corepart is a flexible nonlinear model to parameterize complicated coefficients of the macro-part. To this end, an ARX-like linear structure is constructed as the macro-part by using Taylor expansion; while the coefficients are parameterized by a multi-input-multi-output (MIMO) nonlinear model in the core-part. Nevertheless, it is no easy solution to identify nonlinear systems using the quasi-ARX models, though it is equipped with a useful structure. Followed by requirements of real applications, the identification is expected to interpret properties of the nonlinear system and hold the principle of simplicity. One effective approach to this challenge is to divide the model parameters into two parts: the nonlinear parameters and the linear parameters. The nonlinear parameters mean those interpretable ones, such as translation and dilation parameters of wavelet basis function, which can be determined by using prior knowledge. When the nonlinear parameters are fixed, the quasi-ARX model can be transformed linear in parameters. These linear parameters are the ones to fit the data, which can be estimated by linear regression methods. Furthermore, the quasi-ARX model is meaningful to nonlinear polynomial system identification, which often contains a big number of candidate monomial terms. The identified quasi-ARX model inspires a pre-processing approach to evaluate significance of each monomial term, which is helpful to reduce the candidate pool efficiently. In this thesis, investigations are firstly made on nonlinear parameter estimation with clustering partition and grid partition method, where wavelet network (WN) and neurofuzzy network (NFN) are included as the core-part of the model, respectively. Then the linear parameter is estimated by means of kernel method, where radial basis function network (RBFN) is incorporated. Finally, neural network (NN) is embedded in the quasi-ARX model, which is identified and provides a pre-screening scheme for polynomial system identification. i