TABLE OF CONTENTS In the past years many approaches to modelling of nonlinear systems using neural networks and fuzzy models have been proposed 1 [3]. The difficulties associated with these black-box modelling techniques are mainly related to the curse of dimensionality 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 [4]. 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 [5]. The Gaussian process prior approach was first introduced in [6] and revised in [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.
The number of tunable parameters for a Gaussian process model is dramatically reduced in comparison to typical neural networks. These parameters need to be trained from training data or provided from prior knowledge. In common with neural networks, a Gaussian process model is a black-box model, which will not provide any physical knowledge about the modelled system. However, a Gaussian process model will provide an estimate of the variance of its predicted output, which can be interpreted...
