The concept for Gaussian process model based system identification toolbox

Abstract

The Gaussian process model is an example of a flexible, probabilistic, nonparametric model with uncertainty predictions. It can be used for the modelling of complex nonlinear systems and recently it has also been used for dynamic systems identification. A need for the supporting software, in particular for dynamic system identification, has been recognised. Consequently, a Matlab toolbox concept for Gaussian Process based System Identification was generated. The use of the supporting software is illustrated with a nonlinear dynamic system identification example. INTRODUCTIONWhile there are numerous methods for the identification of linear dynamic systems from measured data, the nonlinear systems identification requires more sophisticated approaches. The most common choices include artificial neural networks, fuzzy models etc. Gaussian process (GP) models present an emerging, complementary method for a nonlinear system identification.The GP model is a probabilistic, non-parametric black-box model. It differs from most of the other black-box identification approaches as it does not try to approximate the modelled system by fitting the parameters of the selected basis functions but rather searches for the relationship among measured data. GP models are closely related to approaches such as Support Vector Machines and specially Relevance Vector Machines [1].The output of the GP model is a normal distribution, expressed in terms of mean and variance. The mean value represents the most likely output and the variance can be interpreted as the measure of its confidence. The obtained variance, which depends on the amount and quality of the available identification data, is important information, distinguishing the GP model from other methods. The GP model structure determination is facilitated as only the covariance function and the regressors of the model need to be selected. Another potentially useful attribute of the GP model is the possibility to include various kinds of prior knowledge into the model, see e.g. [2] for the incorporation of local models and the static characteristic. Also the number of model parameters, which need to be optimised is smaller than in other black-box identification approaches. The disadvantage of the method is the potential computational burden for optimization, which increases with the amount of data and the number of regressors.The GP model was first used for solving a regression problem in the late seventies, but it gained popularity within the machine learning community in the late nineties of the twentieth century. Results of a possible implementation of the GP model for the identification of dynamic systems were presented only recently, e.g. [3,4]. The investigation of the model with uncertain inputs, which enables the propagation of uncertainty through the model, is given in [5] and illustrated in [6].If the method is to be interesting for the practical use in the nonlinear black-box identification, a supporting software, available for the users in the community, is a necessity. Th...

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