Abstract
Gaussian process models provide a probabilistic non-parametric modelling approach for black-box identification of nonlinear dynamic systems. The Gaussian processes can highlight areas of the input space where prediction quality is poor, due to the lack of data or its complexity, by indicating the higher variance around the predicted mean. Gaussian process models contain noticeably less coefficients to be optimized. This chapter illustrates possible application of Gaussian process models within model predictive control. The extra information provided by the Gaussian process model is used in predictive control, where optimization of the control signal takes the variance information into account. The predictive control principle is demonstrated via the control of a pH process benchmark.
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Allgöwer, F., Badgwell, T.A., Qin, S.J., Rawlings, J.B., Wright, S.J.: Nonlinear predictive control and moving horizon estimation - an introductory overview. In: Frank, P.M. (ed.) Advances in control: highlights of ECC 1999, pp. 391–449. Springer, Heidelberg (1999)
Allgöwer, F., Zheng, A. (eds.): Nonlinear Model Predictive Control, Progress in system and control theory, vol. 26. Birkhäuser, Basel (2000)
Girard, A., Rasmussen, C.E., Quinonero Candela, J., Murray-Smith, R. (eds.): Gaussian Process Priors With Uncertain Inputs & Application to Multiple-Step Ahead Time Series Forecasting, NIPS 15, Vancouver, Canada. MIT Press, Cambridge (2003)
Girard, A., Murray-Smith, R.: Gaussian Process: Prediction at a noisy input and application to iterative multiple-step ahead forecasting of time-series. In: Murray-Smith, R., Shorten, R. (eds.) Switching and Learning in Feedback Systems. Springer, Heidelberg (2004)
Gregorčič, G., Lightbody, G.: Internal model control based on a Gaussian process prior model. In: Proceedings of ACC 2003, Denver, CO, pp. 4981–4986 (2003)
Johansen, T.A., Foss, B.A., Sorensen, A.V.: Non-linear predictive control using local models - applied to a batch fermentation process. Control Eng. Practice 3(3), 389–396 (1995)
Henson, M.A., Seborg, D.E.: Adaptive Nonlinear Control of a pH Neutralization Process. IEEE Trans. Control System Technology 2(3), 169–183 (1994)
Kavšek-Biasizzo, K., Škrjanc, I., Matko, D.: Fuzzy predictive control of highly nonlinear pH process. Computers & chemical engineering 21, Supp. 1997, S613–S618 (1997)
Kerrigan, E.C., Maciejowski, J.M.: Soft constraints and exact penalty functions in model predictive control. In: Control 2000 Conference, Cambridge (2000)
Kocijan, J., Girard, A., Banko, B., Murray-Smith, R.: Dynamic Systems Identification with Gaussian Processes. In: Proceedings of 4th Mathmod, Vienna, pp. 776–784 (2003)
Kocijan, J., Likar, B., Banko, B., Girard, A., Murray-Smith, R., Rasmussen, C.E.: A case based comparison of identification with neural network and Gaussian process models. In: Preprints of IFAC ICONS Conference, Faro, pp. 137–142 (2003)
Kouvaritakis, B., Cannon, M. (eds.): Nonlinear predictive control, Theory and practice. IEEE Control Engineering Series, vol. 61. IEEE, Los Alamitos (2001)
Maciejowski J.M., Predictive control with constraints. Pearson Education Limited, Harlow, (2002)
Murray-Smith, R., Girard, A.: Gaussian Process priors with ARMA noise models. In: Irish Signals and Systems Conference, Maynooth, pp. 147–152 (2001)
Murray-Smith, R., Johansen, T.A., Shorten, R.: On transient dynamics, off-equilibrium behaviour and identification in blended multiple model structures. In: European Control Conference, Karlsruhe (1999), BA-14
Murray-Smith, R., Sbarbaro, D.: Nonlinear adaptive control using nonparametric Gaussian process prior models. In: Proc. IFAC Congress, Barcelona (2002)
Nørgaard, M., Ravn, O., Poulsen, N.K., Hansen, L.K.: Neural networks for modeling and control of dynamic systems. Springer, London (2000)
Qin, S.J., Badgwell, T.A.: An overview of industrial model predictive control technology. In: Kantor, J.C., Garcia, C.E., Carnahan, B. (eds.) Fifthe international conference on Chemical process control, AChE and CACHE, pp. 232–256 (1997)
Qin, S.J., Badgwell, T.A.: An overview of nonlinear model predictive control applications. In: Allgöwer, F., Zheng, A. (eds.) Nonlinear model predictive control, pp. 369–392. Birkhauser Verlag (2000)
Rasmussen, C.E.: Evaluation of Gaussian Processes and other Methods for Non- Linear Regression, Ph.D. Disertation, Graduate department of Computer Science, University of Toronto, Toronto (1996)
Solak, E., Murray-Smith, R., Leithead, W.E., Leith, D.J., Rasmussen, C.E.: Derivative observations in Gaussian Process models of dynamic systems, NIPS 15, Vancouver, Canada. MIT Press, Cambridge (2003)
Williams, C.K.I.: Prediction with Gaussian processes: From linear regression to linear prediction and beyond. In: Jordan, M.I. (ed.) Learning in Graphical Models, pp. 599–621. Kluwer Academic, Dordrecht (1998)
Young, R.E., Bartusiak, R.D., Fontaine, R.W.: Evolution of an industrial nonlinear model predictive controller. Preprints on Chemical Process Control - CPC VI, CACHE, Tucson, AZ, 399-401 (2001)
Zheng, A., Morari, M.: Stability of model predictive control with mixed constraints. IEEE Trans. Autom. Control 40(19), 1818–1823 (1995)
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Kocijan, J., Murray-Smith, R. (2005). Nonlinear Predictive Control with a Gaussian Process Model. In: Murray-Smith, R., Shorten, R. (eds) Switching and Learning in Feedback Systems. Lecture Notes in Computer Science, vol 3355. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30560-6_8
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DOI: https://doi.org/10.1007/978-3-540-30560-6_8
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