An Adaptive Fuzzy Predictive Control Based on Support Vector Regression

In this paper, an adaptive fuzzy Generalized Predictive Control (GPC) is proposed for nonlinear systems via Takagi-Sugeno system based Support Vector Regression (TS-SVR). The adaptive T-S fuzzy model is created using a support vector regression while the online learning procedure is obtained in two steps: first, the antecedent parameters of the TS-SVR are initialized using a k-means clustering and then iteratively adjusted using a back-propagation algorithm. Next, a sequential minimal optimization (SMO) algorithm is used to obtain the consequent parameters. Furthermore, the new TS fuzzy model is integrated into the GPC in order to control nonlinear systems. The performance of the proposed adaptive TS-SVR GPC controller is investigated by controlling the continuous stirred tank reactor (CSTR) system. The proposed TS-SVR GPChas shown good performance and efficiently controlled the nonlinear plant.

[1]  Uzay Kaymak,et al.  Model predictive control using fuzzy decision functions , 2001, IEEE Trans. Syst. Man Cybern. Part B.

[2]  David W. Clarke,et al.  Generalized predictive control - Part I. The basic algorithm , 1987, Autom..

[3]  Vojislav Kecman,et al.  Bias Term b in SVMs Again , 2004, ESANN.

[4]  J. Mercer Functions of Positive and Negative Type, and their Connection with the Theory of Integral Equations , 1909 .

[5]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[6]  Helen H. Lou,et al.  Fuzzy model predictive control , 2000, IEEE Trans. Fuzzy Syst..

[7]  Corinna Cortes,et al.  Support-Vector Networks , 1995, Machine Learning.

[8]  Federico Girosi,et al.  An Equivalence Between Sparse Approximation and Support Vector Machines , 1998, Neural Computation.

[9]  Vojislav Kecman,et al.  On the equality of kernel AdaTron and sequential minimal optimization in classification and regression tasks and alike algorithms for kernel machines , 2003, ESANN.

[10]  Jung-Hsien Chiang,et al.  Support vector learning mechanism for fuzzy rule-based modeling: a new approach , 2004, IEEE Trans. Fuzzy Syst..

[11]  Dr. Hans Hellendoorn,et al.  An Introduction to Fuzzy Control , 1996, Springer Berlin Heidelberg.

[12]  Serdar Iplikci,et al.  Support Vector Machines Based Generalized Predictive Control of Chaotic Systems , 2006, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[13]  V. Kecman,et al.  Iterative Single Data Algorithm for Training Kernel Machines from Huge Data Sets: Theory and Performance , 2005 .

[14]  Stephen A. Billings,et al.  International Journal of Control , 2004 .

[15]  Mahesan Niranjan,et al.  Uncertainty in geometric computations , 2002 .

[16]  E. Camacho Constrained generalized predictive control , 1993, IEEE Trans. Autom. Control..

[17]  Tshilidzi Marwala,et al.  An adaptive fuzzy predictive control of nonlinear processes based on Multi-Kernel least squares support vector regression , 2018, Appl. Soft Comput..

[18]  Tshilidzi Marwala,et al.  A new T-S fuzzy model predictive control for nonlinear processes , 2017, Expert Syst. Appl..

[19]  J. MacQueen Some methods for classification and analysis of multivariate observations , 1967 .

[21]  Lotfi A. Zadeh,et al.  Outline of a New Approach to the Analysis of Complex Systems and Decision Processes , 1973, IEEE Trans. Syst. Man Cybern..

[22]  Chia-Feng Juang,et al.  A Fuzzy System Constructed by Rule Generation and Iterative Linear SVR for Antecedent and Consequent Parameter Optimization , 2012, IEEE Transactions on Fuzzy Systems.

[23]  János Abonyi,et al.  Effective optimization for fuzzy model predictive control , 2004, IEEE Transactions on Fuzzy Systems.

[24]  C. Mohtadi,et al.  Properties of generalized predictive control , 1987, Autom..

[25]  Michael Vogt,et al.  Active-Set Methods for Support Vector Machines , 2005 .

[26]  Chia-Feng Juang,et al.  TS-fuzzy system-based support vector regression , 2009, Fuzzy Sets Syst..

[27]  Vincent Wertz,et al.  Fuzzy Logic, Identification and Predictive Control , 2004 .

[28]  H. Su,et al.  Generalized Predictive Control with Online Least Squares Support Vector Machines , 2007, ACTA AUTOMATICA SINICA.

[29]  Serdar Iplikci,et al.  Online trained support vector machines‐based generalized predictive control of non‐linear systems , 2006 .

[30]  Jianbin Qiu,et al.  Sliding mode control for non-linear systems by Takagi-Sugeno fuzzy model and delta operator approaches , 2017 .

[31]  Xinping Guan,et al.  Nonlinear generalized predictive control based on online least squares support vector machines , 2014, Nonlinear Dynamics.

[32]  Vladimir N. Vapnik,et al.  The Nature of Statistical Learning Theory , 2000, Statistics for Engineering and Information Science.