Robustly stable model predictive control based on parallel support vector machines with linear kernel

Abstract

Robustly stable multi-step-ahead model predictive control (MPC) based on parallel support vector machines (SVMs) with linear kernel was proposed. First, an analytical solution of optimal control laws of parallel SVMs based MPC was derived, and then the necessary and sufficient stability condition for MPC closed loop was given according to SVM model, and finally a method of judging the discrepancy between SVM model and the actual plant was presented, and consequently the constraint sets, which can guarantee that the stability condition is still robust for model/plant mismatch within some given bounds, were obtained by applying small-gain theorem. Simulation experiments show the proposed stability condition and robust constraint sets can provide a convenient way of adjusting controller parameters to ensure a closed-loop with larger stable margin.

Keywords

parallel support vector machines / model predictive control / stability / robustness

References

[1] MIAO Qi, WANG Shi-fu. Nonlinear model predictive control based on support vector regression[C]// Proceedings of the 1st International Conference on Machine Learning and Cybernetics. Beijing: 2002: 1657–1661.

[2] WangY.-h., HuangD.-x., GaoD.-j., et al.. Nonlinear predictive control based on support vector machine[J]. Information and Control, 2004, 33(2): 133-136

[3] ZhangH.-r., HanZ.-z., LiC.-gang.. Support vector machine based nonlinear model predictive control[J]. Systems Engineering and Electronics, 2003, 25(3): 330-334

[4] ZhongW.-m., PiD.-ying.. SVM with linear kernel function based nonparametric model identification and model algorithmic control[C]. IEEE Proceedings on Networking, Sensing and Control, 2005, Tucson, IEEE Press: 982-987

[5] ZhongW.-m., HeG.-l., PiD.-y., et al.. SVM with polynomial kernel function based nonlinear model one-step-ahead predictive control [J]. Chinese Journal of Chemical Engineering, 2005, 13(3): 373-379

[6] ZhongW.-m., PiD.-y., SunY.-xian.. Support vector machine based nonlinear model multi-step-ahead optimizing predictive control[J]. Journal of Central South University of Technology, 2005, 12(5): 591-595

[7] LiP., LiG., MengL.-bai.. Generalized predictive control for dual-control systems[J]. Journal of Central South University of Technology: Natural Science, 2003, 34(4): 386-389

[8] MaciejowskiJ. M.Predictive Control with Constraints[M], 2002, London, Prentice Hall

[9] VapnikV. N.The Nature of Statistical Learning Theory[M], 1995, New York, Springer-Verlag

[10] SmolaA. J., SchölkopfB.A tutorial on support vector regression[R], 1998, London, Royal Holloway College, London University

[11] ZhuJ.Intelligent Predictive Control and its Application[M], 2002, Hangzhou, Zhejiang University Press