A Gaussian Process Based Model Predictive Controller for Nonlinear Systems with Uncertain Input-Output Delay


Article Preview

In this paper, we propose a Model Predictive Controller (MPC) based on Gaussian process for nonlinear systems with uncertain delays and external Gaussian disturbances. We investigate the ability of Gaussian process based MPC on handling the variable delay that follows a Gaussian distribution through a properly selected observation horizon. To test the effectiveness of this approach, comparisons are made for the proposed Gaussian process based MPC and RBF (Radial Basis Function) neural networks by analyzing the time complexity and control performance. In simulations, two experiments are designed to verify the results of different systems, including a first-order nonlinear plant and a second-order nonlinear plant with variable delays and Gaussian noises. It is demonstrated that the proposed approach may achieve the desired results.



Edited by:

Krzysztof Galkowski and Yun-Hae Kim




G. Shen and Y. Cao, "A Gaussian Process Based Model Predictive Controller for Nonlinear Systems with Uncertain Input-Output Delay", Applied Mechanics and Materials, Vols. 433-435, pp. 1015-1020, 2013

Online since:

October 2013





[1] B. Shafai and H. Sadaka, Robust Stability and Stabilization of Uncertain Delay Systems, 2012 American Control Conference Fairmont Queen Elizabeth, Montréal, Canada June 27-June 29, (2012).

DOI: https://doi.org/10.1109/acc.2012.6315698

[2] H. K. Khalil, Nonlinear Systems (Third Edition). Upper Saddle River, NJ: Prentice-Hall, (2002).

[3] Min Han, Predictive Control Based on Feedforward Neural Network for Strong Nonlinear System, Proceedings of International Joint Conference on Neural Networks, Montreal, Canada, July 31 - August 4, (2005).

DOI: https://doi.org/10.1109/ijcnn.2005.1556254

[4] Joseph Hall, Carl Rasmussen and Jan Maciejowski, Modelling and Control of Nonlinear Systems using Gaussian Processes with Partial Model Information, 51st IEEE Conference on Decision and Control December 10-13, 2012. Maui, Hawaii, USA.

DOI: https://doi.org/10.1109/cdc.2012.6426746

[5] G. Skolidis and G. Sanguinetti, Bayesian multitask classification with Gaussian process priors, IEEE Trans. Neural Netw., vol. 22, no. 12, p.2011–2021, Dec. (2011).

DOI: https://doi.org/10.1109/tnn.2011.2168568

[6] J. Murillo-Fuentes and F. Perez-Cruz, Gaussian process regressors for multiuser detection in DS-CDMA systems, IEEE Trans. Commun., vol. 57, no. 8, p.2339–2347, Aug. (2009).

DOI: https://doi.org/10.1109/tcomm.2009.08.070450

[7] F. Perez-Cruz, J. Murillo-Fuentes, and S. Caro, Nonlinear channel equalization with Gaussian processes for regression, IEEE Trans. Signal Process., vol. 56, no. 10, p.5283–5286, Oct. (2008).

DOI: https://doi.org/10.1109/tsp.2008.928512

[8] C. E. Rasmussen, Gaussian Processes for Machine Learning,. the MIT Press, 2006, ISBN 026218253X.

[9] Dongbing Gu, Spatial Gaussian Process Regression With Mobile Sensor Networks, IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL. 23, NO. 8, AUGUST (2012).

DOI: https://doi.org/10.1109/tnnls.2012.2200694

[10] Shaowei Wang, Multiuser Detection with Sparse Spectrum Gaussian Process Regression, IEEE COMMUNICATIONS LETTERS, VOL. 16, NO. 2, FEBRUARY (2012).

DOI: https://doi.org/10.1109/lcomm.2011.120211.111508

[11] Mark A. Kon , Neural Networks Radial Basis Functions and Complexity, Boston University and University of Warsaw.

[12] Mohsen Heidarinejad, Jinfeng Liu and Panagiotis D. Christofides, Distributed Model Predictive Control of Switched Nonlinear Systems, 2012 American Control Conference Fairmont Queen Elizabeth, Montréal, Canada June 27-June 29, (2012).

DOI: https://doi.org/10.1109/acc.2012.6314950

[13] Cahyantari Ekaputri, Arief Syaichu-Rohman, Implementation Model Predictive Control (MPC) Algorithm-3 for Inverted Pendulum, 2012 IEEE Control and System Graduate Research Colloquium (ICSGRC 2012).

DOI: https://doi.org/10.1109/icsgrc.2012.6287146

[14] JUS Kocijan, Roderick Murray-Smith, Carl Edward Rasmussen, Agathe Girard, Gaussian Process Model Based Predictive Control, American Control Conference Boston, Massachuselts June 30 -July 2, (2004).

[15] P. D. Christofides, J. Liu, and D. Mu˜ noz de la Pe˜ na, Networked and Distributed Predictive Control: Methods and Nonlinear Process Network Applications, Advances in Industrial Control Series. Springer-Verlag, London, England, (2011).

[16] Young-Sup Hwang , Bang, Sung-Yang, An efficient method to construct a radial basis function neural network classifier and its application unconstrained handwritten digit recognition, Pattern Recognition, 1996, Proceedings of the 13th International Conference on Volume: 4 Digital Object Identifier: 10. 1109/ICPR. 1996. 547643 Publication Year: 1996 , Page(s): 640 - 644 vol. 4.

DOI: https://doi.org/10.1109/icpr.1996.547643