Estimating nonlinear dynamics in nonlinear state-space models

This work aims at developing methods for estimating nonlinear state-space models of the form
x(t+1)=f(x(t),u(t))
y(t)=g(x(t))
based on a combination of ideas from the statistical learning community used to solve nonlinear regression problems on one hand, and methods to handle dynamics from the system identification community on the other hand. The proposed approach consists of the following steps: (1) model the dynamics of the system based on the concept of best linear approximation; 2) estimate the nonlinear states by solving a least squares problem; 3) model the nonlinearities by using regression methods such as Neural Networks and Support Vector Machines.