ADAPTIVE FUZZY OUTPUT FEEDBACK TRACKING CONTROL FOR A CLASS OF NONLINEAR TIME-VARYING DELAY SYSTEMS WITH UNKNOWN BACKLASH-LIKE HYSTERESIS

Document Type: Research Paper

Authors

Department of Electrical Engineering, Shahid Bahonar University, Kerman, Iran

Abstract

This paper considers the problem of adaptive output feedback tracking control for a class of nonstrict-feedback nonlinear systems with unknown time-varying delays and unknown backlash-like hysteresis. Fuzzy logic systems are used to estimate the unknown nonlinear functions. Based on the Lyapunov–Krasovskii method, the control scheme is constructed by using the backstepping and adaptive technique. The proposed adaptive controller guarantees that all the closed-loop signals are semiglobally uniformly ultimately bounded and the tracking error can converge to a small neighborhood of the origin. Finally, Simulation results further show the effectiveness of the proposed approach.

Keywords


[1] B. Chen, C. Lin, X. Liu and K. Liu, Observer-based adaptive fuzzy control for a class of
nonlinear delayed systems, IEEE Trans. Syst., Man, Cybern. Syst., 46(1) (2016), 27{36.
[2] B. Chen, X. Liu and K. Liu and C. Lin, Direct adaptive fuzzy control of nonlinear strict-
feedback systems, Automatica, 45(6) (2009), 1530{1535.
[3] B. Chen, X. P. Liu, S. S. Ge and C. Lin, Adaptive fuzzy control of a class of nonlinear systems
by fuzzy approximation approach, IEEE Trans. Fuzzy Syst, 20(6) (2012), 1012{1021.
[4] S. S. Ge, F. Hong and T. H. Lee, Adaptive neural network control of nonlinear systems with
unknown time delays, IEEE Trans. Autom. Control, 48(11) (2003), 2004{2010.
[5] F. Gmez Estern, A. Barreiro, J. Aracil and F. Gordillo, Robust generation of almost-periodic
oscillations in a class of nonlinear systems, Int. J. Robust and Control, 16(18) (2006),
863{890.
[6] C. Hua and X. Guan, Output feedback stabilization for time-delay nonlinear interconnected
systems using neural networks, IEEE Trans. Neural Netw., 19(4) (2008), 673{688.
[7] L. R. Hunt and G. Meyer, Stable inversion for nonlinear systems, Automatica, 33(8) (1997),
1549{1554.
[8] M. Krstic, I. Kanellakopoulos and P. V. Kokotovic, Nonlinear and Adaptive Control Design,
New York, NY, USA: Wiley, 1995.
[9] H. Lee and M. Tomizuka, Robust adaptive control using a universal approximation for SISO
nonlinear systems, IEEE Trans. Fuzzy Syst., 8(1) (2001), 95{106.
[10] Y. Li and S. C. Tong, Adaptive fuzzy output-feedback stabilization control for a class of
switched nonstrict-feedback nonlinear systems, IEEE Trans. Cybern., 99 (2016), 1{10.
[11] Y. Li, S. C. Tong, Y. Liu and T. Li, Adaptive fuzzy robust output feedback control of nonlinear
systems with unknown dead zones based on a small-gain approach, IEEE Trans. Fuzzy Syst,
22(1) (2014), 164-176.
[12] Z. Liu, G. Lai, Y. Zhang, X. Chen and C. L. P. Chen, Adaptive neural control for a class of
nonlinear time-varying delay systems with unknown hysteresis, IEEE Trans. Neural Netw.
Learn. Syst, 25(12) (2014), 2129{2140.
[13] A. E. Ougli and B. Tidhaf, Optimal type-2 fuzzy adaptive control for a class of uncertain
nonlinear systems using an LMI approach, Int. J. Innov. Comput. I., 11(3) (2015), 851-863.
[14] B. Ren, S. S. Ge, C. Y. Su and T. H. Lee, Adaptive neural control for a class of uncertain
nonlinear systems in pure-feedback form with hysteresis input, IEEE Trans. Syst., Man,
Cybern. Syst., 39(2) (2009), 431{443.
[15] C. Y. Su, M. Oya and H. Hong, Stable adaptive fuzzy control of nonlinear systems preceded
by unknown backlash-like hysteresis, IEEE Trans. Fuzzy Syst, 11(1) (2003), 1{8.
[16] C. Y. Su, Y. Stepanenko, J. Svoboda and T. P. Leung, Robust adaptive control of a class
of nonlinear systems with unknown backlash-like hysteresis, IEEE Trans. Autom. Control,
45(12) (2000), 2427{2432.
[17] X. Tan and J. S. Baras, Modelling and control of hysteresis in magnetostrictive actua-
tors,Automatica, 40(9) (2004), 1469{1480.
[18] G. Tao and P. V. Kokotovic, Adaptive control of plants with unknown hysteresis, IEEE Trans.
Autom. Control, 40(2) (1995), 200{212.

[19] G. Tao and P. V. Kokotovic, Continuous-time adaptive control of systems with unknown
backlash, IEEE Trans. Autom. Control, 40(6) (2002), 1083{1087.
[20] S. C. Tong and Y. Li, Adaptive fuzzy output feedback tracking backstepping control of strict
feedback nonlinear systems with unkown dead zones, IEEE Trans. Fuzzy Syst, 20(1) (2012),
168{180.
[21] S. C. Tong, Y. Li and S. Sui, Adaptive Fuzzy Tracking Control Design for SISO Uncertain
Non-Strict Feedback Nonlinear Systems, IEEE Trans. Fuzzy Syst., 24(6) (2016), 1441{1454.
[22] S. C. Tong, S. Sui and Y. Li, Adaptive fuzzy decentralized output stabilization for stochas-
tic nonlinear large-scale systems with unknown control directions, IEEE Trans. Fuzzy Syst,
22(5) (2014), 1365{1372.
[23] S. C. Tong, X. L. He and H. G. Zhang, A combined backstepping and small-gain approach to
robust adaptive fuzzy output feedback contro, IEEE Trans. Fuzzy Syst, 17(5) (2009), 1059{
1069.
[24] H. Wang, B. Chen, K. Liu, X. Liu and C. Lin, Adaptive neural tracking control for a class of
nonstrict-feedback stochastic nonlinear systems with unknown backlash-like hysteresis, IEEE
Trans. Neural Netw. Learn. Syst., 25(5) (2014), 947{958.
[25] M. Wang, B. Chen, X. Liu and P. Shi, Adaptive fuzzy tracking control for a class of perturbed
strict-feedback nonlinear time-delay systems, Fuzzy Set. Syst., 159(8) (2008), 949{967.
[26] Y. Yang and C. Zhou, Adaptive fuzzy H stabilization for strict-feedback canonical non-
linear systems via backstepping and small-gain approach, IEEE Trans. Fuzzy Syst, 13(1)
(2005),104{114.
[27] J. Yu, P. Shi, H. Yu, B. Chen and C. Lin, Approximation-based discrete-time adaptive position
tracking control for interior permanent magnet synchronous motors, IEEE Trans. Cybern,
45(7) (2015), 1363{1371.
[28] X. Zhou, P. Shi and X. Zheng, Fuzzy adaptive control design and discretization for a class
of nonlinear uncertain systems, IEEE Trans. Cybern, 46(6) (2016), 1476{1483.
[29] Q. Zhou, P. Shi, S. Xu and H. Li, Adaptive output feedback control for nonlinear time-delay
systems by fuzzy approximation approach, IEEE Trans. Fuzzy Syst, 21(2) (2013), 301{313.
[30] J. Zhou, C. Wen and Y. Zhang, Adaptive backstepping control of a class of uncertain non-
linear systems with unknown backlash-like hysteresis, IEEE Trans.Autom. Control, 49(10)
(2004), 1751{1759.
[31] J. Zhou, C. Wen and T. Li, Adaptive output feedback control of uncertain nonlinear systems
with hysteresis nonlinearity, IEEE Trans. Autom. Control, 57(10) (2012), 2627{2633.