On-line identification with regularised Evolving Gaussian process

The on-line identification of nonlinear dynamical system with the regularised nonparametric regression approach is considered. The model structure is a nonlinear finite impulse response (NFIR) based on a Gaussian process (GP). The online estimation of the tuning parameters of the GP model leads to an Evolving Gaussian process whose structure adapts to the current dynamics of the measured system. The GP regression is a kernel method which requires storing the past measurements. The kernel-based on-line system identification is implementable only with a constraint on the amount of data stored. The on-line identification method combines together the forgetting factor for discounting old data and the moving window which neglects the highly discounted data. As a consequence, the online-identification problem may be ill-posed due to the discounted data. A regularisation approach is introduced for the estimation of the tuning parameters in order to avoid the ill-posed identification problem. The performance of the online identification method is demonstrated with an illustrative example.