Abstract
A support vector machine with guadratic polynomial kernel function based nonlinear model multi-step-a-head optimizing predictive controller was presented. A support vector machine based predictive model was established by black-box identification. And a quadratic objective function with receding horizon was selected to obtain the controller output. By solving a nonlinear optimization problem with equality constraint of model output and boundary constraint of controller output using Nelder-Mead simplex direct search method, a sub-optimal control law was achieved in feature space. The effect of the controller was demonstrated on a recognized benchmark problem and a continuous-stirred tank reactor. The simulation results show that the multi-step-ahead predictive controller can be well applied to nonlinear system, with better performance in following reference trajectory and disturbance-rejection.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
SHU Di-qian. Predictive Control System and its Application [M]. Beijing: China Machine Press, 1996. (in Chinese)
Morari M, Lee J H. Model predictive control: past, present and future[J]. Computer and Chemical Engineering, 1999, 23(4–5): 667–682.
Liu B, Shen Q, Su H Y, et al. A nonlinear predictive control algorithm based on fuzzy online modeling and discrete optimization systems[J]. Proc IEEE of Man and Cybernetics, 2003, 1: 816–821.
Kambhampati C, Mason J D, Warwick K. A stable one-step-ahead predictive control of non-linear systems [J]. Automatica, 2000, 36: 485–495.
ZHU Jing. Intelligent Predictive Control and Application [M]. Hangzhou: Zhejiang University Press, 2002. (in Chinese)
Vapnik V N. The Nature of Statistical Learning Theory[M]. New York: Springer-Verlag, 1995.
Cortes C. Prediction of Generalization Ability in Learning Machines[D]. Rochester: Univ New York, USA, 1995.
Smola A J, Schölkopf B. A tutorial on support vector regression [R]. London: Royal Holloway College, London Univ, 1998.
Müller K R, Smola A J. Predicting time series with support vector machines [A]. Proc of ICANN[C]. Springer LNCS 1327, 1997.
Miao Q, Wang S F. Nonlinear model predictive control based on support vector regression[A]. Proceedings of the 1st International Conference on Machine Learning and Cybernetics[C]. Beijing, 2002.
Suykens J A K. Nonlinear modelling and support vector machines[J]. IEEE Transactions on Instrumentation and Measurement Technology, 2001, 1: 287–294.
Suykens J A K, Vandewalle J, de Moor B. Optimal control by least squares support vector machines[J]. Neural Networks, 2001, 14(1): 23–35.
Narendra K S, Parthasarathy K. Identification and control of dynamic systems using neural networks [J]. IEEE Transaction on Neural Networks, 2000, 1: 4–27.
Lehman B, Bentsman J, Lunel S V, et al. Vibrational control of nonlinear time lag systems with bounded delay: averaging theory, stabilizability, and transient behavior[J]. IEEE Transactions on Automatic Control, 1994, 39: 898–912.
Cao Y Y, Frank P M. Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach [J]. IEEE Transactions on Fuzzy Systems, 2000, 8(2): 200–211.
Author information
Authors and Affiliations
Corresponding author
Additional information
Foundation item: Project (2002CB312200) supported by the National Key Fundamental Research and Development Program of China
Rights and permissions
About this article
Cite this article
Zhong, Wm., Pi, Dy. & Sun, Yx. Support vector machine based nonlinear model multi-step-ahead optimizing predictive control. J Cent. South Univ. Technol. 12, 591–595 (2005). https://doi.org/10.1007/s11771-005-0128-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11771-005-0128-4
Key words
- nonlinear model predictive control
- support vector machine
- nonlinear system identification
- kernel function
- nonlinear optimization