Gaussian process approach for modelling of nonlinear systems

Parametric modelling principals such as neural networks, fuzzy models and multiple model techniques have been proposed for modelling of nonlinear systems. Research effort has focused on issues such as the selection of the structure, constructive learning techniques, computational issues, the curse of dimensionality, off-equilibrium behaviour, etc. To reduce these problems, the use of non-parametrical modelling approaches have been proposed. This paper introduces the Gaussian process (GP) prior approach for the modelling of nonlinear dynamic systems. The relationship between the GP model and the radial basis function neural network is explained. Issues such as selection of the dimension of the input space and the computation load are also discussed. The GP modelling technique is demonstrated on an example of the nonlinear hydraulic positioning system.