Indirect Adaptive Interval Type-2 Fuzzy PI Sliding Mode Control for a Class of Uncertain\ Nonlinear Systems

Document Type: Research Paper

Authors

1 Department of Electrical Engineering, Center of Excellence on Soft Computing and Intelligent Information Processing, Ferdowsi University of Mash- had, Iran

2 Department of Electrical Engineering, Cen- ter of Excellence on Soft Computing and Intelligent Information Processing, Fer- dowsi University of Mashhad, Iran

Abstract

Controller design remains an elusive and challenging problem for
uncertain nonlinear dynamics. Interval type-2 fuzzy logic systems (IT2FLS) in
comparison with type-1 fuzzy logic systems claim to effectively handle system
uncertainties especially in the presence of disturbances and noises, but lack a
formal mechanism to guarantee performance. In contrast, adaptive sliding mode
control (ASMC) provides a robust mechanism to provide system stability against
parameter changes and uncertainties, but suffers from chattering phenomenon.
In this paper, a stable indirect adaptive interval type-2 fuzzy PI sliding mode
controller (AIT2FSMC) is investigated for a class of nonlinear systems in the
presence of system's unmodeled dynamics and external disturbances. The added
Proportional Integral (PI) structure is used to further attenuate the chattering
problem that is common in sliding mode control systems. The interval type-2
fuzzy adaptation law adjusts the consequent parameters of the rules based on a
Lyapunov synthesis approach. Mathematical analysis proves the closed loop
asymptotic stability, while benefiting from human expert knowledge to improve
transient response of the system. Application to two nonlinear systems verifies
the robustness of the proposed AIT2FSMC approach in the presence of
uncertainties and bounded external disturbances, especially when disturbances
have fast changes and large magnitudes.

Keywords


bibitem{1}
M. R. Akbarzadeh-T and R. Shahnazi, {it Direct adaptive fuzzy pi sliding mode control of systems with unknown but bounded disturbances}, Iranian Journal of Fuzzy Systems, {bf 3(2)} (2006), 33-52.

bibitem{2}
M. R. Akbarzadeh-T., K. J. Emami and N. Pariz, {it Adaptive discrete-time fuzzy sliding mode control for anti-lock braking systems},  Proceedings in Fuzzy Information Processing Society, North American, (2002), 554-559.

bibitem{3}
K. J. Astrom  and B. Wittenmark, {it Adaptive control}, Second Edition, Addison-Wesley Pub Co, Newyork, 1994.

bibitem{4}
W. M. Bessa, A. S. de Paula and M. A. Savi, {it Adaptive fuzzy sliding mode control of a chaotic pendulum with noisy signals}, ZAMM - Journal of Applied Mathematics and Mechanics, {bf 94(3)} (2013), 256-263.

bibitem{5}
O. Castillo, R. Martínez-Marroquín, P. Melin, F. Valdez and J. Soria, {it Comparative study of bio-inspired algorithms applied to the optimization of type-1 and type-2 fuzzy controllers for an autonomous mobile robot}, Information Sciences, {bf 192} (2012), 19-38.

bibitem{6}
N. R. Cazarez-Castro, L. T. Aguilar and O. Castillo, {it Designing type-1 and type-2 fuzzy logic controllers via fuzzy lyapunov synthesis for nonsmooth mechanical systems}, Engineering Applications of Artificial Intelligence, {bf 25(5)} (2012), 971-979.

bibitem{7}
C. C. Chiang  and C. C. Yang, {it Robust adaptive fuzzy sliding mode control for a class of uncertain nonlinear systems with unknown dead-zone}, IEEE International Conference on Fuzzy Systems, Vancouver, BC, (2006), 492-497.

bibitem{8}
W. Chi-Hsu, C. Chun-Sheng and L. Tsu-Tian, {it Dynamical optimal training for interval type-2 fuzzy neural network (T2FNN)},  IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, {bf 34(3)} (2004), 1462-1477.

bibitem{9}
K. Chung-Chun, C. Ti-Hung and H. Liang-Chih, {it Adaptive fuzzy sliding mode control for a class of underactuated systems}, IEEE International Conference on Fuzzy Systems, Jeju Island, (2009), 1791-1796.

bibitem{10}
M. Ghaemi and M. R. Akbarzadeh-T, {it Optimal design of adaptive interval type-2 fuzzy sliding mode control using genetic algorithm}, 2nd International Conference on Control, Instrumentation, and Automation, Shiraz, Iran, (2011), 626-631.

bibitem{11}
M. Ghaemi, M. R. Akbarzadeh-T and M. Jalaeian-F, {it Adaptive interval type-2 fuzzy pi sliding mode control with optimization of membership functions using genetic algorithm}, 2nd International eConference on Computer and Knowledge Engineering, Mashhad, Iran, (2012), 123-128.

bibitem{12}
H. F. Ho, Y. K. Wong, and A. B. Rad, {it Adaptive fuzzy sliding mode control design: Lyapunov approach}, 5th Asian Conference in Control, Melbourne, Australia, (2004), 1502-1507.

bibitem{13}
H. F. Ho, Y. K. Wong and A. B. Rad, {it Adaptive fuzzy sliding mode control with chattering elimination for nonlinear SISO systems}, Simulation Modelling Practice and Theory, {bf 17(7)} (2009), 1199-1210.

bibitem{14}
M. Y. Hsiao, T. H. S. Li, J. Z. Lee, C. H. Chao and S. H. Tsai, {it Design of interval type-2 fuzzy sliding-mode controller}, Information Sciences, {bf 178(6)} (2008), 1696-1716.

bibitem{15}
N. N. Karnik and J. M. Mendel, {it Centroid of a type-2 fuzzy set}, Information Sciences, {bf 132(1-4)} (2001), 195-220.

bibitem{16}
N. N. Karnik and J. M. Mendel, {it Type-2 fuzzy logic systems: type-reduction},  IEEE International Conference on Systems, Man, and Cybernetics, San Diego, CA, (1998), 2046-2051.

bibitem{17}
N. N. Karnik, J. M. Mendel and L. Qilian, {it Type-2 fuzzy logic systems}, IEEE Transactions on Fuzzy Systems, {bf 7(6)} (1999), 643-658.

bibitem{18}
Y. K. Kim  and G. J. Jeon, {it Error reduction of sliding mode control using sigmoid-type nonlinear interpolation in the boundary layer},
International Journal of Control, Automation, and Systems, {bf 2(4)} (2004), 523-529.

bibitem{19}
T. C. Lin, {it Based on interval type-2 fuzzy-neural network direct adaptive sliding mode control for SISO nonlinear systems}, Communications in Nonlinear Science and Numerical Simulation, {bf 15(12)} (2010), 4084-4099.

bibitem{20}
T. C. Lin, H. L. Liu and M. J. Kuo, {it Direct adaptive interval type-2 fuzzy control of multivariable nonlinear systems}, Engineering Applications of Artificial Intelligence, {bf  22(3)} (2009), 420-430.

bibitem{21}
Y. Maldonado, O. Castillo and P. Melin, {it Particle swarm optimization of interval type-2 fuzzy systems for FPGA applications}, Applied Soft Computing, {bf 13(1)} (2013), 496-508.

bibitem{22}
J. M. Mendel, {it Advances in type-2 fuzzy sets and systems}, Information Sciences, {bf 177(1)} (2007), 84-110.

bibitem{23}
J. M. Mendel, R. I. John and F. Liu, {it Interval type-2 fuzzy logic systems made simple}, IEEE Transactions on Fuzzy Systems, {bf 14(6)} (2006), 808-821.

bibitem{24}
J. M. Mendel and R. I. B. John, {it Type-2 fuzzy sets made simple}, IEEE Transactions on Fuzzy Systems, {bf 10(2)} (2002), 117-127.

bibitem{25}
L. Qilian and J. M. Mendel, {it Interval type-2 fuzzy logic systems: theory and design}, IEEE Transactions on Fuzzy Systems, {bf 8(5)} (2000), 535-550.

bibitem{26}
W. Rong-Jong, {it Fuzzy sliding-mode control using adaptive tuning technique}, Industrial Electronics, IEEE Transactions on, {bf 54} (2007),  586-594.

bibitem{27}
R. Sepúlveda, O. Montiel, O. Castillo and P. Melin, {it Embedding a high speed interval type-2 fuzzy controller for a real plant into an FPGA}, Applied Soft Computing, {bf 12(3)} (2012), 988-998.

bibitem{28}
R. Shahnazi and M. R. Akbarzadeh-T, {it PI adaptive fuzzy control with large and fast disturbance rejection for a class of uncertain nonlinear systems}, IEEE Transactions on Fuzzy Systems, {bf16(1)} (2008), 187-197.

bibitem{29}
J. E. Slotine and W. Li, {it Applied nonlinear control}, Prentice Hall, Inc.: Englewood Cliffs,
New Jersy, 1991.

bibitem{30}
L. Tie-Shan, T. Shao-Cheng and G. G. Feng, {it A novel robust adaptive-fuzzy-tracking control for a class of nonlinear multi-input/multi-output systems},  IEEE Transactions on Fuzzy Systems, {bf 18(1)} (2010), 150-160.

bibitem{31}
L. Tsung-Chih, C. Ming-Che, M. Roopaei and B. R. Sahraei, {it Adaptive type-2 fuzzy sliding mode control for chaos synchronization of uncertain chaotic systems},  IEEE International Conference on Fuzzy Systems (FUZZ), Barcelona, (2010), 1-8.

bibitem{32}
L. Tsung-Chih and L. Tun-Yuan, {it Chaos synchronization of uncertain fractional-order chaotic systems with time delay based on adaptive fuzzy sliding mode control}, IEEE Transactions on Fuzzy Systems, {bf 19(4)} (2011), 623-635.

bibitem{33}
D. Velez-Diaz and T. Yu, {it Adaptive robust fuzzy control of nonlinear systems}, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, {bf 34(3)} (2004), 1596-1601.

bibitem{34}
L. X. Wang, {it A course in Fuzzy systems and control}, Prentice Hall,New Jersy, 1996.

bibitem{35}
L. X. Wang, {it Stable adaptive fuzzy control of nonlinear systems},  IEEE Transactions on Fuzzy Systems, {bf 1(2)} (1992), 146-155.

bibitem{36}
M. Wang, B. Chen and S. L. Dai, {it Direct adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear systems}, Fuzzy Sets and Systems, {bf 158(24)} (2007), 2655-2670.

bibitem{37}
D. Wu and W. W. Tan, {it A simplified type-2 fuzzy logic controller for real-time control}, ISA Transactions, {bf 45(4)} (2006), 503-516.

bibitem{38}
T. Yu, {it Adaptive robust fuzzy control for output tracking},  Proceedings of the American Control Conference, Boston, MA, USA , (2004), 1788-1793.

bibitem{39}
L. A. Zadeh, {it The concept of a linguistic variable and its application to approximate reasoning--I}, Information Sciences, {bf 8(3)} (1975), 199-249.

bibitem{40}
C. Zhongze, S. Changhong and Z. Huiling, {it Adaptive fuzzy sliding mode control algorithm for a non-affine nonlinear system}, Industrial Informatics, IEEE Transactions on, {bf 3} (2007),  302-311.