Adaptive Predictive Controllers Using a Growing and Pruning RBF Neural Network

Document Type: Research Article


Department of Automation and Instrumentation, Petroleum University of Technology, Tehran, I.R. IRAN


An adaptive version of growing and pruning RBF neural network has been used to predict the system output and implement Linear Model-Based Predictive Controller (LMPC) and Non-linear Model-based Predictive Controller (NMPC) strategies. A radial-basis neural network with growing and pruning capabilities is introduced to carry out on-line model identification.An Unscented Kalman Filter (UKF) algorithm with an exponential time-varying forgetting factor has been presented to enable the neural network model to track any time-varying process dynamic changes. An adaptive NMPC has been designed based on the sequential quadratic programming technique. The paper makes use of a dynamic linearization approach to extract a linear model at each sampling time instant so as to develop an adaptive LMPC. The servo and regulating performances of the proposed adaptive control schemes have been illustrated on a non-linear Continuous Stirred Tank Reactor (CSTR) as a benchmark problem. The simulation results demonstrate the capability of the proposed identification strategy to effectively identify compact, accurate and transparent model for the CSTR process. It is shown that the proposed adaptive NMPC controller presents better improvement with faster response time for both servo and regulatory control objectives in comparison with the proposed adaptive LMPC, an adaptive generalized predictive controller based on Recursive Least Squares (RLS) algorithm and well-tuned PID controllers.  


 [1] Morari M., Lee J.H., Model Predictive Control: Past, Present and Future, Computers and Chemical Engineering, 21, p. 965 (1977).

[2] Qin S.J., Badgwell T.A., "An overview of Industrial Model Predictive Control Technology", Fifth International Conference on Chemical Process Control, AIChE, p. 232 (1997).

[3] Narendra K.S., Parthasarathy K., Identification and Control of Dynamical Systems Using Neural Networks, IEEE Trans. on Neural Networks, 1(1), p. 4 (1990).

[4] Gori M., Tesi A., On the Problem of Local Minima in Backpropagation, IEEE Trans. on Pattern Analysis and Machine Intelligence, 14(1), p. 76 (1992).

[5] Chen S., Billings S.A., Cowan C.F.N., Grant P.M., Practical Identification of  NARMAX Models Using Radial Basis Functions, Int. J. Control, 52(6), p. 1327 (1990).

[6] S. Chen and A. Billings, Neural Networks for Nonlinear Dynamic System Modeling and Identification, Int. J. Control, 56(2), p. 319 (1992).

[7] Girosi F., Poggio T., Networks and the Best Approximation Property, Biological Cybernetics, 63, p. 169 (1990).

[8] Sundararajan N., Saratchandran P., Yingwei L., Radial Basis Function Neural Networks with Sequential Learning: MRAN and its Applications, River Edge: Singapore; World Scientific: NJ, (1999).

[9] Yingwei L., Sundararajan N., and Saratchandran P., A Sequential Learning Scheme for Function Approximation Using Minimal Radial Basis Function (RBF) Neural Networks, Neural Computation, 9, p. 461 (1997).

[10] Huang G.B., Saratchandran P., and Sundararajan N., A Generalized Growing and Pruning RBF (GGAP-RBF) Neural Network for Function Approximation, IEEE Trans. Neural Networks, 16(1), p. 57 (2005).

[11] Julier S.J., Uhlmann J.K., "A New Extension of the Kalman Filter to Non-Linear Systems", in Proc. of AeroSense: The 11th Int. Symp. A.D.S.S.C., (1997).

[12] Nishida K., Yamauchi K., Omori T., "An On-line Learning Algorithm with Dimension Selection using Minimal Hyper Basis Function Networks", SICE Annual Conference in Sapporo, August 4-6, (2004).

[13] Huang G.-B., Saratchandran P., Sundararajan N., An Efficient Sequential Learning Algorithm for Growing and Pruning RBF (GAP-RBF) Networks, IEEE Transactions on systems, man, and cybernetics, part B, 34(6), December (2004).

[14] Wang Y., Huang G.-B., Saratchandran P., Sundararajan N., "Time Series Study of GGAP-RBF Network: Predictions of Nasdaq Stock and Nitrate Contamination of Drinking Wate"r, Proceedings of International Joint Conference on Neural Networks, Montreal, Canada, July 31 - August 4, (2005).

[15] Julier S.J., Uhlmann J.K., Durrant-Whyte H., "A New Approach for Filtering Non-Linear Systems", Proceedings of the American Control Conference, p. 1628 (1995).

[16] Narendra K.S., Mukhopadhyay S., Adaptive Control Using Neural Networks and Approximate Models, IEEE Trans. On neural networks, 8, p. 475 (1999).

[17] Powell M.J.D., A Fast Algorithm for Nonlinearly Constrained Optimization Calculations, Numerical Analysis, G.A.Watson ed., "Lecture Notes in Mathematics",  Springer Verlag, 630, (1978).

[18] Gill P.E., MurrayW., Wright, M.H. Numerical Linear Algebra and  Optimization, 1, Addison Wesley, (1991).

[19] Clarke D.W., Mohtadi C., Tuffs. P.S., Generalized Predictive Control. Part I. The Basic Algorithm, Automatica, 23(2), p. 137 (1987).

[20] Nikravesh M., “Dynamic Neural Network Control”, Ph.D. Dissertation,University of South Carolina, Columbia ,SC, (1994).

[21] Perry R.H., Chilton C.H., “Chemical Engineering Handbook”, 5th ed., McGraw-Hill, New York, (1973).

[22] Piovoso M., Kosanovich K., Rokhlenko V., Guez A., "A Comparison of Three Nonlinear Controller  Designs Applied to a Nonadiabatic First Order Exothermic Reaction in a CSTR", Proceedings of American Control  Conference, Chicago IL, p. 490 (1992).