×

zbMATH — the first resource for mathematics

Adaptive hybrid type-2 intelligent sliding mode control for uncertain nonlinear multivariable dynamical systems. (English) Zbl 1221.93046
Summary: A new adaptive hybrid interval type-2 Fuzzy Neural Network (FNN) controller incorporating sliding mode and Lyapunov synthesis approaches is proposed in this paper to handle the training data corrupted by noise or rule uncertainties for a class of uncertain nonlinear multivariable dynamic systems. The hybrid adaptive FNN controller, the free parameters of which can be tuned on-line by an output feedback control law and adaptive laws, is a combination of interval type-2 indirect and direct adaptive FNN controllers to meet the requirement of sufficient quality of the sliding mode control. A weighting factor, which can be adjusted based on the trade-off between plant knowledge and control knowledge, is included when combining the control efforts of the indirect adaptive FNN controller and the direct adaptive FNN controller. The overall adaptive control scheme guarantees the global stability of the resulting closed-loop system in the sense that all signals involved are uniformly bounded. The mass-spring-damper nonlinear system is fully illustrated to track sinusoidal signals. The resulting adaptive hybrid interval type-2 FNN control system shows better performance than the adaptive hybrid type-1 FNN control system; it reduces both the tracking error and the control effort and it is more flexible in the design process.

MSC:
93B12 Variable structure systems
93C42 Fuzzy control/observation systems
93C35 Multivariable systems, multidimensional control systems
92B20 Neural networks for/in biological studies, artificial life and related topics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Lin, T.-C.; Liu, H.-L.; Kuo, M.-J., Direct adaptive interval type-2 fuzzy control of multivariable nonlinear systems, Engineering applications of artificial intelligence, 22, 420-430, (2009)
[2] Lin, T.-C.; Kuo, M.-J.; Hsu, C.-H., Robust adaptive tracking control of multivariable nonlinear systems based on interval type-2 fuzzy approach, International journal of innovative computing, information and control, 6, 3A, 941-961, (2010)
[3] Noroozi, N.; Roopaei, M.; Zolghadri Jahromi, M., Adaptive fuzzy sliding mode control scheme for uncertain systems, Communications in nonlinear science and numerical simulation, 14, 11, 3978-3992, (2009) · Zbl 1221.93155
[4] Noroozi, N.; Roopaei, M.; Karimaghaee, P.; Safavi, A.A., Simple adaptive variable structure control for unknown chaotic systems, Communications in nonlinear science and numerical simulation, 15, 3, 707-727, (2010) · Zbl 1221.93156
[5] Roopaei, M.; Zolghadri, M.; Meshksar, S., Enhanced adaptive fuzzy sliding mode control for uncertain nonlinear systems, Communications in nonlinear science and numerical simulation, 14, 9, 3670-3681, (2009) · Zbl 1221.93157
[6] Roopaei, M.; Zolghadri, M.; John, R.; Lin, T.-C., Unknown nonlinear chaotic gyros synchronization using adaptive fuzzy sliding mode control with unknown dead-zone input, Communications in nonlinear science and numerical simulation, 15, 2536-2545, (2010) · Zbl 1222.93123
[7] Roopaei, M.; Jahromi, M.Z.; Jafari, S., Adaptive gain fuzzy sliding mode control for the synchronization of nonlinear chaotic gyros, Chaos, 19, 013125, (2009) · Zbl 1311.93049
[8] Roopaei, M.; Jahromi, M.Z., Synchronization of two different chaotic systems using novel adaptive fuzzy sliding mode control, Chaos, 18, 033133, (2008) · Zbl 1309.34075
[9] N. Noroozi, M. Roopaei, V. Emilia Balas, T.-C. Lin, Observer-based adaptive variable structure control and synchronization of unknown chaotic systems, in: Applied Computational Intelligence and Informatics, SACI ’09. 5th International Symposium, 2009, pp. 71-76.
[10] Chen, B.S.; Lee, C.H.; Chang, Y.C., H1 tracking design of uncertain nonlinear SISO systems: adaptive fuzzy approach, IEEE transactions on fuzzy systems, 4, 1, 32-43, (1996)
[11] Chen, B.S.; Tseng, C.S.; Uang, H.J., Mixed H2/H1 fuzzy output feedback control design for nonlinear dynamical systems: an LMI approach, IEEE transactions on fuzzy systems, 8, 3, 249-265, (2000)
[12] Nguang, S.K.; Shi, P., H1 fuzzy output feedback control design for nonlinear systems: an LMI approach, IEEE transactions on fuzzy systems, 11, 3, 331-340, (2003)
[13] Tseng, C.S.; Chen, B.S., H1 decentralized fuzzy model reference tracking control design for nonlinear interconnected systems, IEEE transactions on fuzzy systems, 9, 6, 795-809, (2001)
[14] Yang, Y.; Zhou, C., Adaptive fuzzy H1 stabilization for strict-feedback canonical nonlinear systems via backstepping and small-gain approach, IEEE transactions on fuzzy systems, 13, 1, 104-114, (2005)
[15] Boyd, S.; Ghaoui, E.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in system and control theory, (1994), SIAM Philadelphia, PA · Zbl 0816.93004
[16] Mendel, J.M., Computing derivatives in interval type-2 fuzzy logic systems, IEEE transactions on fuzzy systems, 12, 1, 84-98, (2004)
[17] Wang, J.S.; Lee, C.S.G., Self-adaptive neuro-fuzzy inference systems for classification application, IEEE transactions on fuzzy systems, 10, 6, 790-802, (2002)
[18] Z. Kovacic, M. Balenovic, S. Bogdan, Sensitivity based self learning fuzzy logic control for a servo system, IEEE Control Systems, June (1998).
[19] Golea, N.; Golea, A.; Benmahammed, K., Fuzzy model reference adaptive control, Fuzzy sets and systems, 137, 3, 353-366, (2003) · Zbl 1037.93053
[20] Hojati, M.; Gazor, S., Hybrid adaptive fuzzy identification and control of nonlinear systems, IEEE transactions on fuzzy systems, 10, 2, 198-210, (2002)
[21] Lee, H.; Tomizuka, M., Robust adaptive control using a universal approximator for SISO nonlinear systems, IEEE transactions on fuzzy systems, 8, 95-106, (2001)
[22] Wang, C.H.; Cheng, C.S.; Lee, T.T., Dynamical optimal training for interval type-2 fuzzy neural network (T2FNN), IEEE transactions on systems, man and cybernetics, part B, 34, 3, 2004, (2004)
[23] Kheireddine, C.; Lamir, S.; Mouna, G.; hier, B., Indirect adaptive interval type-2 fuzzy control for nonlinear systems, International journal of modeling, identification and control, 2, 2, (2007)
[24] Lee, C.C., Fuzzy logic in control system: fuzzy logic controller—parts I, II, IEEE transactions on systems, man and cybernetics, 20, 404-435, (1990)
[25] Wang, L.X., A course in fuzzy systems and control, (1997), Prentice-Hall Englewood Cliffs, NJ
[26] Kosko, B., Fuzzy systems are universal approximators, IEEE transactions on computer, 43, 11, 1329-1333, (1994) · Zbl 1057.68664
[27] Wang, L.X.; Mendel, M., Fuzzy basis functions universal approximation, and orthogonal least squares learning, IEEE transactions on neural networks, 1, 3, 804-814, (1992)
[28] Narendra, K.S.; Parthasarathy, K., Identification and control of dynamical systems using neural networks, IEEE transactions on neural networks, 1, 1, 4-27, (1990)
[29] Yu, S.H.; Annaswamy, A.M.; White, H., Stable neural controllers for nonlinear dynamic systems, Automatica, 34, 5, 641-650, (1998) · Zbl 0934.93055
[30] Lewis, F.L.; Liu, K.; Yesildirek, A., Neural-net robot controller with guaranteed tracking performance, IEEE transactions on neural networks, 1, 6, 703-715, (1995)
[31] Marino, R.; Tomei, P., Globally adaptive output-feedback control on nonlinear systems, part I: linear parameterization, IEEE transactions on automatic control, 1, 38, 17-32, (1993) · Zbl 0783.93032
[32] Marino, R.; Tomei, P., Globally adaptive output-feedback control on nonlinear systems, part II: nonlinear parameterization, IEEE transactions on automatic control, 1, 38, 33-48, (1993) · Zbl 0799.93023
[33] Rovithakis, G.A.; Christodoulou, M.A., Adaptive control of unknown plants using dynamical neural networks, IEEE transactions on systems, man and cybernetics, 1, 24, 400-412, (1994) · Zbl 1371.93112
[34] Slotine, J.E.; Li, W., Applied nonlinear control, (1991), Prentice-Hall Englewood Cliffs, NJ · Zbl 0753.93036
[35] Tsakalis, K.S.; Ioannou, P.A., Linear time-varying systems, (1993), Prentice-Hall Englewood Cliffs, NJ · Zbl 0737.93041
[36] Sastry, S.; Bodson, M., Adaptive control stability, convergence, and robustness, (1989), Prentice-Hall Englewood Cliffs, NJ · Zbl 0721.93046
[37] Wang, L.X., Stable adaptive fuzzy control of nonlinear systems, IEEE transactions on fuzzy systems, 1, 1, 146-155, (1993)
[38] Wang, L.X., Adaptive fuzzy systems and control: design and stability analysis, (1994), Prentice-Hall Englewood Cliffs, NJ
[39] Leu, Y.G.; Lee, T.T.; Wang, W.Y., Observer-based adaptive fuzzy-neural control for unknown nonlinear dynamical systems, IEEE transactions on systems, man and cybernetics, 29, 583-591, (1999)
[40] Wang, C.-H.; Liu, H.-L.; Lin, T.-C., Direct adaptive fuzzy-neural control with state observer and supervisory control for unknown nonlinear dynamical systems, IEEE transactions on fuzzy systems, 10, 1, 39-49, (2002)
[41] Wang, C.-H.; Lin, T.-C.; Lee, T.-T.; Liu, H.-L., Adaptive hybrid intelligent control for uncertain nonlinear dynamical systems, IEEE transactions on systems, man and cybernetics, 32, 5, 583-597, (2002)
[42] Itkis, Y., Control systems of variable structure, (1976), Wiley New York
[43] Utkin, V.A., Sliding modes and their applications in variable structure systems, (1978), Mir Moscow
[44] Hung, J.Y.; Gao, W.; Hung, J.C., Variable structure control: a survey, IEEE transactions on industrial electronics, 40, 1, 2-22, (1993)
[45] R. Palm, Sliding mode fuzzy control, in: International Conference on Fuzzy Systems, San Diego, CA, 1992, pp. 519-526.
[46] S.C. Lin, Y.Y. Chen, Design of adaptive fuzzy sliding mode for nonlinear system control, in: International Conference on Fuzzy Systems, Orlando, FL, 1994, pp. 35-39.
[47] Yoo, B.; Ham, W., Adaptive fuzzy sliding mode control of nonlinear system, IEEE transactions on fuzzy systems, 6, 2, 315-321, (1998)
[48] Wang, W.Y.; Chan, M.L.; James Hsu, C.C.; Lee, T.T., \(H_\infty\) tracking-based sliding mode control for uncertain nonlinear systems via adaptive fuzzy-neural approach, IEEE transactions on systems, man and cybernetics, 32, 483-492, (2002)
[49] Chang, Y.C., Adaptive fuzzy-based tracking control for nonlinear SISO systems via VSS and \(H^\infty\) approaches, IEEE transactions on fuzzy systems, 9, 278-292, (2001)
[50] Tong, S.; Li, H.-X., Fuzzy adaptive sliding-mode control for MIMO nonlinear systems, IEEE transactions on fuzzy systems, 11, 3, 345-359, (2003)
[51] Chiang, C.C.; Wu, C.H., Observer-based adaptive fuzzy sliding mode control of uncertain multiple-input multiple-output nonlinear systems, IEEE transactions on fuzzy systems, 23-26, (2007)
[52] Lin, W.S.; Chen, C.S., Robust adaptive sliding mode control using fuzzy modelling for a class of uncertain MIMO nonlinear systems, IEE process control: theory and applications, 149, 3, (2002)
[53] Aloui, S.; Pages, O.; El Hajjaji, A.; Chaari, A.; Koubaa, Y., Improved observer-based adaptive fuzzy tracking control for MIMO nonlinear systems, IEEE transactions on fuzzy systems, 20-24, (2009)
[54] Roopaei, M.; Elmilia, V.; Lin, T.-C.; Seifi, A., Adaptive gain fuzzy sliding mode control in uncertain MIMO nonlinear system, Nonlinear studies, 16, 3, 261-273, (2009) · Zbl 1177.93027
[55] Leu, Y.G.; Wang, W.Y.; Lee, T.T., Robust adaptive fuzzy-neural controllers for uncertain nonlinear systems, IEEE transactions on robotics and automation, 15, 805-817, (1999)
[56] W.S. Lin, C.S. Chen, Sliding-mode-based direct adaptive fuzzy controller design for a class of uncertain multivariable nonlinear systems, in: Proceedings of the American Control Conference, 2002, pp. 8-10.
[57] Y.Q. Zheng, Y.J. Liu, S.C. Tong, T.S. Li, Combined adaptive fuzzy control for uncertain mimo nonlinear systems, in: Proceedings of the 2009 American Control Conference, 2009, pp. 10-12.
[58] Kim, D.; Yang, H.; Hong, S., An indirect adaptive fuzzy sliding-mode control for decoupled nonlinear systems, IEEE transactions on fuzzy systems, 6, 2, 315-321, (2003)
[59] Li, H.X.; Tong, S., A hybrid adaptive fuzzy control for a class of nonlinear MIMO systems, IEEE transactions on fuzzy systems, 11, 1, 24-34, (2003)
[60] Karnik, N.N.; Mendel, J.M.; Liang, Q., Type-2 fuzzy logic systems, IEEE transactions on fuzzy systems, 7, 643-658, (1999)
[61] Mendel, J.M.; John, R.I.B., Type-2 fuzzy sets made simple, IEEE transactions on fuzzy systems, 10, 117-127, (2000)
[62] Hsiao, M.Y.; Li, T.H.S.; Lee, J.Z.; Chao, C.H.; Tsai, S.H., Design of interval type-2 fuzzy sliding-mode controller, Information science, 178, 1696-1716, (2008) · Zbl 1139.93019
[63] Mendel, J.M., Type-2 fuzzy sets and systems: an overview, IEEE computational intelligence magazine, 2, 1, 20-29, (2007)
[64] Mendel, J.M.; John, R.I.; Liu, F., Interval type-2 fuzzy logic systems made simple, IEEE transactions on fuzzy systems, 14, 6, 808-821, (2006)
[65] Lin, T.-C., Analog circuit fault diagnosis under parameter variations based on type-2 fuzzy logic systems, International journal of innovative computing, information and control, 6, 5, 2137-2158, (2010)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.