Multiple-step-ahead prediction in control systems with Gaussian process models and TS-fuzzy models

In this paper one-step-ahead and multiple-step-ahead predictions of time series in disturbed open loop and closed loop systems using Gaussian process models and TS-fuzzy models are described. Gaussian process models are based on the Bayesian framework where the conditional distribution of output measurements is used for the prediction of the system outputs. For one-step-ahead prediction a local process model with a small past horizon is built online with the help of Gaussian processes. Multiple-step-ahead prediction requires the knowledge of previous outputs and control values as well as the future control values. A ‘‘naive’’ multiple-step-ahead prediction is a successive one-step-ahead prediction where the outputs in each consecutive step are used as inputs for the next step of prediction. A global TS-fuzzy model is built to generate the nominal future control trajectory for multiple-step-ahead prediction. In the presence of model uncertainties a correction of the so computed control trajectory is needed. This is done by an internal feedback between the two process models. The method is tested on disturbed time invariant and time variant systems for different past horizons. The combination of the TS-fuzzy model and the Gaussian process model together with a correction of the control trajectory shows a good performance of the multiple-step-ahead prediction for systems with uncertainties. r 2007 Elsevier Ltd. All rights reserved.