Gaussian process approaches to nonlinear modelling for control

In the past years many approaches to modelling of nonlinear systems using neural networks and fuzzy modelshave been proposed. The difficulties associated with these black-box modelling techniques are mainly related to the curse of dimension ality and lack of transparency of the model. The local modelling approach has been proposed to increase transparency as well as reduce the curse of dimensionality. Difficulties related to partitioning of the operating space, structure determination, local model identification and off-equilibrium dynamics are the main drawbacks of such local modelling techniques. To improve the off-equilibrium behaviour, the use of non-parametric probabilistic models, such as Gaussian process priors was proposed. The Gaussian process prior approach was first introduced in Reference 6 and revised in References 7-9. The ability to make a robust estimation in the transient region, where only a limited number of data points is available, is one of the advantages of the Gaussian process in comparison to the local model network.