Abstract
In this paper, a nonlinear model predictive control strategy which utilizes a probabilistic sparse kernel learning technique called relevance vector regression (RVR) and particle swarm optimization with controllable random exploration velocity (PSO-CREV) is applied to a catalytic continuous stirred tank reactor (CSTR) process. An accurate reliable nonlinear model is first identified by RVR with a radial basis function (RBF) kernel and then the optimization of control sequence is speeded up by PSO-CREV. Additional stochastic behavior in PSO-CREV is omitted for faster convergence of nonlinear optimization. An improved system performance is guaranteed by an accurate sparse predictive model and an efficient and fast optimization algorithm. To compare the performance, model predictive control (MPC) using a deterministic sparse kernel learning technique called Least squares support vector machines (LS-SVM) regression is done on a CSTR. Relevance vector regression shows improved tracking performance with very less computation time which is much essential for real time control.
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References
S. Qin, A. T. Badgwell. A survey of industrial model predictive control technology. Control Engineering Practice, 2003, 11(7):733–764.
M. A. Henson. Nonlinear model predictive control: current status and future directions. Computers & Chemical Engineering, 1998, 23(2):187–202.
J. A. Rossiter. Model Based Predictive Control: A Practical Approach. New York: CRC press, 2003.
Y. Liu, Y. Gao, Z. Gao, et al. Simple nonlinear predictive control strategy for chemical processes using sparse kernel learning with polynomial form. Industrial & Engineering Chemistry Research, 2010, 49(17):8209–8218.
N. Bhat, T. J. Mcavoy. Use of neural nets for dynamic modeling and control of chemical process systems. Computers and Chemical Engineering, 1990, 14(5):573–583.
D. C. Psichogios, L. H. Ungar. Direct and indirect model based control using artificial neural network. Industrial & Engineering Chemistry Research, 1991, 30(12):2564–2573.
K. J. Hunt, K. Sbarbaro, R. Zbikowski, et al. Neural network for control systems — a survey. Automatica, 1992, 28(6):1083–1120.
J. S. Taylor, N. Cristianini. Kernel Methods for Pattern Analysis. Cambridge: Cambridge University Press, 2004.
C. M. Bishop. Pattern Recognition and Machine Learning. New York: Springer-Verlag, 2006.
V. Vapnik. Statistical Learning Theory. New York: Wiley, 1998.
M. E. Tipping. The relevance vector machine. Advances in Neural Information Processing Systems. Cambridge: MIT Press, 2000:652–658.
M. E. Tipping. Sparse bayesian learning and the relevance vector machine. Journal of Machine Learning Research, 2001, 1(3):211–244.
Y. Liu, W. Wang. Sparse Kernel Learning based nonlinear predictive controllers. Applied mathematics and information sciences, 2011, 5(2):195–201.
G. Camps-Valls, M. Martinez-Ramon, J. L. Rojo-Alvarez, et al. Nonlinear system identifiation with composite relevance vector machines. IEEE Signal Processing Letters, 2007, 14(4):279–282.
I. Psorakis, T. Damoulas, M. A. Girolami. Multiclass relevance vector machines: sparsity and accuracy. IEEE Transactions on Neural Networks, 2010, 21(10):1588–1598.
P. Samui, V. R. Mandla, A. Krishna, et al. Prediction of rainfall using support vector machine and relevance vector machine. Earth Science India, 2011, 4(4):188–200.
J. Q. Candela, L. K. Hansen. Time serier prediction based on the relevance vector machine with adaptive kernels. Proceedings of IEEE International Conference on Aquostics, Speech and Signal Processing. New York: IEEE, 2003:985–988.
P. Samui, P. Kurup. Use of relevance vector machine for prediction of overconsolidation ratio. International Journal of Geomechanics, 2011, 13(1):26–32.
M. A. Nicolaou, H. Gunes, M. Pantic. Output-associative RVM regression for dimensional and continuous emotion prediction. Image and Vision Computing, 2012, 30(3):186–196.
S. Tai. An annealing dynamical learning-based relevance vector regression algorithm for housing price forecasting. Journal of Information and Computational Science, 2011, 8(14):3313–3319.
P. K. Wong, Q. Xu, C. M. Vong, et al. Rate-dependent hysteresis modeling and control of a Piezostage using online support vector machine and relevance vector machine. IEEE Transactions on Industrial Electronics, 2012, 59(4):1988–2001.
R. C. Eberhart, J. Kennedy. A new optimizer using particle swarm theory. Proceedings of the 6th International Symposium on Micro Machine and Human Science. New York: IEEE, 1995:39–43.
J. Kennedy, R. C. Eberhart. Particle swarm optimization. Proceedings of IEEE International Conference on Neural Networks. New York: IEEE, 1995:1942–1948.
H. Yoshida, K. Kawata, Y. Fukuyama, et al. A particle swarm optimization for reactive power and voltage control considering voltage stability. Proceedings of IEEE International Conference on Intelligent System Applications to Power Systems. Rio de Janeiro, 1999:117–121.
L. Messerschmidt, A. P. Engelbrecht. Learning to play games using a PSO-based competitive learning approach. IEEE Transactions on Evolutionary Computation, 2004, 8(3):280–288.
C. M. Bishop, M. E. Tipping. Variational relevance vector machines. Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence. San Francisco: Morgan Kaufmann Publishers Inc., 2000:46–53.
J. O. Berger. Statistical Decision Theory and Bayesian Analysis. New York: Springer-Verlag, 1980.
X. Chen, Y. Li. Neural network predictive control for mobile robot Using PSO with controllable random exploration velocity. International Journal of Intelligent Control and Systems, 2007, 12(3):217–229.
X. Chen, Y. Li. A modified PSO structure resulting in high exploration ability with convergence guaranteed. IEEE Transactions on Systems, Man and Cybernetics, 2007, 37(5):1271–1289.
K. D. Brabanter, P. Karsmakers, F. Ojeda, et. al. LS-SVM Lab Toolbox User’s Guide (Version 1.8). Belgium: Heverlee, 1980.
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M. GERMIN NISHA received her M.E degree in Process Control and Instrumentation Engineering from Annamalai University in 2005, and currently she is pursuing her Ph.D. at Electrical Engineering Department, Indian Institute of Technology (IIT), Roorkee. Her research interests are in the area of control and artificial intelligence.
G. N. PILLAI received his M.Tech. degree from Regional Engineering College, Kurukshetra, India, in 1989, and Ph.D. degree from Indian Institute of Technology (IIT), Kanpur, India, in December 2001. He did his postdoctoral studies from Ulster University, U.K., in 2003. Currently, he is an associate professor at Electrical Engineering Department, Indian Institute of Technology (IIT), Roorkee, India since 2004. Before joining IIT Roorkee, he was a faculty member of Electrical Engineering Department, NIT Kurukshetra, India. His interests are in the areas of power systems, control and artificial intelligence.
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Germin Nisha, M., Pillai, G.N. Nonlinear model predictive control with relevance vector regression and particle swarm optimization. J. Control Theory Appl. 11, 563–569 (2013). https://doi.org/10.1007/s11768-013-2119-6
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DOI: https://doi.org/10.1007/s11768-013-2119-6