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Nonlinear generalized predictive control based on online least squares support vector machines. (English) Zbl 1345.93068

Summary: For a class of nonlinear discrete systems with unknown parameters, an adaptive direct generalized predictive control method based on online least squares support vector machines (OLS-SVM) is proposed. In the method, the OLS-SVM is used to design the controller directly, and an improved projection algorithm based on the tracking error is introduced to adjust the weights of the OLS-SVM adaptively, so the inverse matrix is avoided in the process of online real-time control. It is proved that the proposed method can make the tracking error converge to a small neighborhood of the origin. Simulation results have shown the correctness and effectiveness of the proposed method.

MSC:

93C10 Nonlinear systems in control theory
93C83 Control/observation systems involving computers (process control, etc.)
93C40 Adaptive control/observation systems
93C55 Discrete-time control/observation systems
39A60 Applications of difference equations
39A30 Stability theory for difference equations
39A24 Almost periodic solutions of difference equations
37M05 Simulation of dynamical systems
37N35 Dynamical systems in control
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[1] Clarke, D.W., Mohtadi, C., Tuffs, P.S.: Generalized predictive control, Part I. The basic algorithm. Automatica 23(2), 137-148 (1987) · Zbl 0621.93032 · doi:10.1016/0005-1098(87)90087-2
[2] Zhang, J., Morris, J.: Nonlinear model predictive control based on multiple local linear model. In: Proceedings of American Control Conference, Arlington, VA, pp. 3503-3508 (2001) · Zbl 1164.93376
[3] Fischer, M., Nelles, O., Isermann, R.: Predictive control based on local linear fuzzy models. Int. J. Syst. Sci. 29(7), 679-697 (1998) · Zbl 0994.93522 · doi:10.1080/00207729808929563
[4] Zhu, J.: Intelligent Predictive Control and Its Application. Zhejiang University Press, Hangzhou (2000). (in Chinese)
[5] Zhang, G.H., Lu, J.H., Chen, J.L.: Fuzzy generalized predictive control and its application. Acta Autom. Sinica 19(1), 9-16 (1993) · Zbl 0779.93066
[6] Shi, W.X.: Studies of adaptive fuzzy generalized predictive control. Ph.D. thesis, Beihang. Univ., Beijing, China (2003) (in Chinese)
[7] Shi, W.X., Huo, W., Wu, H.X.: Direct adaptive fuzzy predictive control for a class of unknown nonlinear discrete systems. Acta Autom. Sinica 30(5), 664-670 (2004) (in Chinese) · Zbl 1498.93405
[8] Chen, Z.W., Wang, H.R.: Nonlinear fuzzy adaptive direct generalized predictive control. Electr. Mach. Control 11(1), 55-59 (2007) (in Chinese) · Zbl 1164.93376
[9] Sun, D.Q., Wu, H.X.: Characteristic modeling and adaptive fuzzy control method of MIMO higher-order linear time-varying systems. J. Astr. 26(6), 677-692 (2005) (in Chinese)
[10] You, Y., Wu, C., You, J.S., Han, Y.H.: DFS forecast control control based on Takagi-sugeno fuzzy logical ratiocination. J. Syst. Simul. 18(5), 1257-1259 (2006) (in Chinese) · Zbl 1134.93419
[11] Mahfouf, M., Abbod, M.F., Linkens, D.A.: Online elicitation of Mamdani-type fuzzy rules via TSK-based generalized predictive control. IEEE Trans. Syst. Man Cybern. Part B 3(3), 465-475 (2003) · doi:10.1109/TSMCB.2003.810901
[12] Li, Q., Qu, B.C., Ge, Z.Q.: Study of fuzzy generalized predictive control algorithm on nonlinear systems. In: First International Conference on Innovative Computing Information Control, vol. 1, pp. 437-440 (2006)
[13] Andone, D., Hossu, A.: Predictive control based on fuzzy model for steam generator. In: 2004 IEEE International Conference on Fuzzy Systems, Budapset, Hungary, pp. 1245-1250 (2004) · Zbl 0621.93032
[14] Yoo, S.J., Choi, Y.H., Park, J.B.: Generalized predictive control based on self-recurrent wavelet neural network for stable path tracking of mobile robots: adaptive learning rates approach. IEEE Trans. Circuits Syst. I Regul. Pap. 53(6), 1381-1394 (2006) · Zbl 1374.93201 · doi:10.1109/TCSI.2006.875166
[15] Dong, N., Chen, Z.Q.: A novel ADP based model-free predictive control. Nonlinear Dyn. 69, 89-97 (2012) · Zbl 1253.93042 · doi:10.1007/s11071-011-0248-3
[16] Eski, i, Temürlenk, A.: Design of neural network-based control systems for active steering system. Nonlinear Dyn. 73, 1443-1454 (2013) · doi:10.1007/s11071-013-0875-y
[17] Yang, J.J., Liu, M., Wu, C.: Genetic algorithm based nonlinear model predictive control method. Control Decis. 18(2), 141-144 (2003) (in Chinese)
[18] Vapnik, V.: The Nature of Statistical Learning Theory. Springer, New York (2000) · Zbl 0934.62009 · doi:10.1007/978-1-4757-3264-1
[19] Tian, J., Gu, H.: Anomaly detection combining one-class SVMs and particle swarm optimization algorithms. Nonlinear Dyn. 61, 303-310 (2010) · Zbl 1204.68173 · doi:10.1007/s11071-009-9650-5
[20] Yuan, X.F., Wang, Y.N., Wu, L.H.: Composite feedforward-feedback controller for generator excitation system. Nonlinear Dyn. 54, 355-364 (2008) · Zbl 1170.93322 · doi:10.1007/s11071-008-9334-6
[21] Liu, B., Su, H.Y., Chu, J.: Predictive control algorithm based on least squares support vector machines. Control Decis. 19(12), 1399-1402 (2004) (in Chinese) · Zbl 1109.68546
[22] Wang, Y.H., Huang, D.X., Gao, D.J., Jin, Y.H.: Nonlinear predictive control based on support vector machine. Inf. Control 33(2), 133-136 (2004) (in Chinese)
[23] Iplikei, S.: Support vector machines-based generalized predictive control. Int. J. Robust Nonlinear Control 16(17), 843-862 (2006) · Zbl 1134.93419 · doi:10.1002/rnc.1094
[24] Zhang, R.D., Wang, S.Q., Li, P.: Support vector machine based predictive control for nonlinear systems. Acta Autom. Sinica 33(10), 1066-1073 (2007) (in Chinese) · Zbl 1164.93326
[25] Li, L.J., Su, H.Y., Chu, J.: Generalized predictive control with online least squares support vector machines. Acta Autom. Sinica 33(11), 1182-1188 (2007) · Zbl 1164.93376 · doi:10.1360/aas-007-1182
[26] Li, H., Huang, L.J.: Generalized predictive control based on LS-SVM inverse system method. In: Proceedings of 8th World Congress On Intelligence Control and Automation, Jinan, China, pp. 2604-2609 (2010)
[27] Ling, A., Ye, S.: Model predictive control for nonlinear distributed parameter systems based on LS-SVM. Asian J. Control 15(6), 1-10 (2013)
[28] Suykens, J.A., Vandewalle, J.: Least squares support vector machine classifiers. Neural Process. Lett. 9(3), 293-300 (1999) · doi:10.1023/A:1018628609742
[29] Guo, J., Chen, Q.W., Zhu, R.J., Hu, W.L.: Adaptive predictive control of a class of nonlinear system. Control Theory Appl. 19(1), 68-72 (2002) (in Chinese) · Zbl 1006.93527
[30] Goodwin, G.C., Sin, K.S.: Adaptive Filtering, Prediction and Control. Dover Publications, New York (2009) · Zbl 1250.93001
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