ADAPTIVE FUZZY TRACKING CONTROL FOR A CLASS OF PERTURBED NONLINEARLY PARAMETERIZED SYSTEMS USING MINIMAL LEARNING PARAMETERS ALGORITHM

Document Type : Research Paper

Authors

School of Science, Xi'an University of Architecture and Technology, Xi'an, 710055, PR China

Abstract

In this paper, an adaptive fuzzy tracking control approach is proposed for a class of single-input
single-output (SISO) nonlinear systems in which the unknown continuous functions may be nonlinearly
parameterized. During the controller design procedure, the fuzzy logic systems (FLS) in Mamdani type are applied to approximate the unknown continuous functions, and then, based on the minimal learning parameters (MLP) algorithm and the adaptive backstepping dynamic surface control (DSC) technique, a new adaptive fuzzy backstepping control scheme
is developed. The main advantages of our approach include: (i) unlike the existing results which deal with the nonlinearly
parameterized functions by using the separation principle, the nonlinearly parameterized functions are lumped into the continuous functions which can be approximated by using the FLS, (ii) only one parameter needs to be adjusted online in controller design procedure, which reduces the online computation burden greatly, and our development is able to eliminate the problem of ''explosion of complexity" inherent in the existing backstepping-based methods. It is proven that
the proposed design method is able to guarantee that all the signals in the closed-loop system are bounded and the tracking error is smaller than a prescribed error bound. Finally, two examples are used to show the effectiveness of the proposed approach.

Keywords

References

[1] B. Chen, X. P. Liu and S. C. Tong, Adaptive fuzzy output tracking control of MIMO nonlinear
uncertain systems, IEEE Trans. Fuzzy Syst., 15 (2) (2007), 287-300.
[2] B. Chen, X. P. Liu, K. F. Liu and C. Lin, Direct adaptive fuzzy control of nonlinear strictfeedback
systems, Automatica, 45 (2009), 1530-1535.
[3] M. Chen, S. S. Ge, B. V. E. How and Y. S. Choo,Robust adaptive position mooring control
for marine vessels, IEEE Trans. Control Syst. Technol., 21 (2013), 395-409.
[4] W. S. Chen and Z. Q. Zhang, Globally stable adaptive backstepping fuzzy control for outputfeedback
systems with unknown high-frequency gain sign, Fuzzy Sets and Systems, 161 (2010),
821-836.
[5] W. S. Chen, L. C. Jiao, R. H. Li and J. Li, Adaptive backstepping fuzzy control for nonlinearly
parameterized systems with periodic disturbances, IEEE Trans. Fuzzy Syst., 18(4) (2010),
674-685.
[6] W. S. Chen and L. C. Jiao, Adaptive tracking for periodically time-varying and nonlinearly parameterized
systems using multilayer neural networks, IEEE Trans. Neural Networks, 21(2))
(2010), 345-351.
[7] H. Deng and M. Krstic, Stochastic nonlinear stabilization, part I: a backstepping design, Syst.
Control Lett., 32 (1997), 143-150.
[8] F. Z. Gao and F. S. Yuan, Adaptive stabilization of stochastic nonholonomic systems with
nonlinear parameterization, Applied Mathematics and Computation, 219 (2013), 8676-8686.
[9] F. Z. Gao, F. S. Yuan and Y. Q. Wu, Adaptive stabilization for a class of stochastic nonlinearly
parameterized nonholonomic systems with unknown control coefficients, Asian Journal
of Control, 16(6) (2014), 1829-1838.
[10] Y. Gao, S. C. Tong and Y. M. Li, Observer-based adaptive fuzzy output constrained control
for MIMO nonlinear systems with unknown control directions, Fuzzy Sets and Systems, 290
(2016), 79-99.
[11] H. Q. Huang, X. P. Liu and K. F. Liu, Adaptive fuzzy tracking control for a class of purefeedback
stochastic nonlinear systems with non-lower triangular structure, Fuzzy Sets and
Systems, 302 (2016), 101-120.
[12] H. B. Ji and H. S. Xi, Adaptive output-feedback tracking of stochastic nonlinear systems,
IEEE Trans. Autom. Control, 51 (2006), 355-360.
[13] M. Krsti´c, I. Kanellakopulos and P.V. Kocotovic, Nonlinear and Adaptive Control Design,
Wiley, New York, 1995.
[14] T. S. Li, G. Feng, Z. J. Zou and Y. J. Liu, Robust adaptive fuzzy tracking control for a class of
MIMO systems: A minimal learning- parameters algorithm, American Control Conference,
(2009), 3106-3111.
[15] W. Lin and C. J. Qian, Adaptive control of nonlinearly parameterized systems: the smooth
feedback case, IEEE Trans. Autom. Control, 47(8) (2002), 1249-1266.
[16] Y. G. Liu, Output-feedback adaptive control for a class of nonlinear systems with unknown
control directions, Acta Automatica Sinica, 33(12) (2007), 1306-1312.
[17] Y. J. Liu, S. C. Tong and W. Wang, Adaptive fuzzy output tracking control for a class of
uncertain nonlinear systems, Fuzzy Sets and Systems, 160 (2009), 2727-2754.
[18] X. B. Liu, R. Ortega, H. Y. Su and J. Chu, Immersion and invariance adaptive control of
nonlinearly parameterized nonlinear systems, American Control Conference, St. Louis, MO,
USA June 10-12, (2009), 1268-1273.
[19] L. J. Long, Z. Wang and J. Zhao, Switched adaptive control of switched nonlinearly parameterized
systems with unstable subsystems, Automatica, 54 (2015), 217-228.
[20] R. Marino and P. Tomei, Global adaptive output-feedback control of nonlinear systems , part
I: linear parameterization, IEEE Trans. Autom. Control, 38(1) (1993), 17-32.
[21] K. S. Narendra and A. M. Annaswamy, Stable Adaptive Systems, Prentice-Hall, Englewood
Cliffs, NJ, 1989.
[22] H. B. Pang and J. Zhao, Adaptive passification and stabilization for switched nonlinearly
parameterized systems, International Journal of Robust and Nonlinear Control, 27 (2017),
1147-1170.
[23] D. Swaroop, J. K. Hedrick, P. P. Yip and J. C. Gerdes, Dynamic surface control of nonlinear
systems, IEEE Trans. Autom. Control, 45(10) (2000), 1893-1899.
[24] L. X.Wang, Adaptive Fuzzy Systems and Control Design and Stability Analysis, NJ: Prentice-
Hall, Englewood Cliffs, 1994.
[25] M. Wang, B. Chen, X. P. Liu and P. Shi, Adaptive fuzzy tracking control for a class of
perturbed strict-feedback nonlinear time-delay systems, Fuzzy Sets and Systems 159 (2008),
949-967.
[26] X. L. Wu, X. J. Wu, X. Y. Luo, Q. M. Zhu and X. P. Guan, Neural network-based adaptive
tracking control for nonlinearly parameterized systems with unknown input nonlinearities,
Neurocomputing, 82 (2012), 127-142.
[27] B. Yao and M. Tomizukai, Adaptive robust control of SISO nonlinear a semi-strict feedback
form, Automatica, 33(5) (1997), 893-900.
[28] Y. S. Yang and C. J. Zhou, Robust adaptive fuzzy tracking control for a class of perturbed
strict-feedback nonlinear systems via small-gain approach, Information Sciences, 170 (2005),
211-234.
[29] S. Yin, S. Ding and H. Luo, Real-time implementation of fault tolerant control system with
performance optimization, IEEE Trans. Ind. Electron., 61 (2014), 2402-2411.
[30] S. Yin, S. Ding, X. Xie and H. Luo, A review on basic data-driven approaches for industrial
process monitoring, IEEE Trans. Ind. Electron., 61 (2014), 6418-6428.
[31] P. P. Yip and J. K. Hedrick, Adaptive dynamic surface control: a simplified algorithm for
adaptive backstepping control of nonlinear systems, Int. J. Control, 71(5) (1998), 959-979.
[32] H. Y. Yue and J. M. Li, Adaptive fuzzy tracking control for a class of perturbed nonlinear timevarying
delays systems with unknown control direction, International Journal of Uncertainty,
Fuzziness and Knowledge-Based Systems, 21 (4) (2013), 497-531.
[33] H. Y. Yue and J. M. Li, Adaptive fuzzy dynamic surface control for a class of perturbed
nonlinear time-varying delay systems with unknown dead-zone, International Journal of Automation
and Computing, 9(5) (2012), 545-554.
[34] H. Y. Yue and S. Q. Yu, Adaptive fuzzy tracking control for a class of stochastic nonlinearly
parameterized systems with distributed input delay, Journal of the Franklin Institute, 353
(2016), 713-734.
[35] T. P. Zhang and S. S. Ge, Adaptive neural control of MIMO nonlinear state time-varying
delay systems with unknown dead-zones and gain signs, Automatica, 43 (2007), 1021-1033.
Iranian Journal of Fuzzy Systems
Volume 15, Issue 3
May and June 2018
Pages 99-116

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