Nonparametric and iterative identification of nonlinear systems

System identification is an important step in system analysis and control. There are no general solutions to nonlinear system identification. This thesis proposes nonparametric and iterative approaches to identify nonlinear systems with different structural assumptions.;For black-box nonlinear systems, classical nonparametric kernel estimation methods are presented to identify nonlinear finite impulse response (NFIR) and nonlinear autoregressive exogenous (NARX) systems. A recursive stochastic approximation algorithm is proposed for NFIR system identification. For NARX systems, an input-to-output exponential stability property is found to be a sufficient condition for the kernel estimates to be convergent. Point-wise convergence analysis is discussed for both types of system, and the asymptotic convergence properties of the algorithms are established under some assumptions. Several examples are provided to illustrate the effectiveness of the kernel estimators.;To optimize the performance of the kernel estimator for finite data samples, a direct weight optimization (DWO) approach is recently presented. In this thesis, the DWO approach is adopted but a different performance criterion is used. The weights are optimized to minimize the probability of an upper bound of squared error to be larger than a certain value. Under the Gaussian noise assumption, the optimization problem is formulated. The solution is found to be fairly simple and easy to compute. The performance is robust in the sense that the noise can be any distribution with a bounded variance. A benchmark system is used to test the performance of the minimal probability estimator, and the results are promising.;The last part of this thesis deals with identification the Hammerstein systems with odd symmetric nonlinear part. Iterative algorithms are proposed to estimate the unknown parameters in the models. The iterative methods are applied to Hammerstein systems with infinite impulse response (IIR) linear part and Hammerstein systems with two common non-smooth nonlinear structure, i.e., saturation and preload. The parameter convergence properties are proved in one iterative step when the data sample is infinite. The simulations verify the fast convergence of the proposed algorithms.