Abstract
This paper proposes an observer-based fuzzy controller for strict-feedback nonlinear systems. A fuzzy state observer is designed to estimate unmeasurable system states via a fuzzy logic system to approximate the unknown nonlinear functions of the system. A tangent prescribed performance function is utilized to gather the tracking error in a small neighborhood of the origin. The control input is designed to deal with the dead-zone property of the system. The proposed controller can guarantee that all the signals in the closed-loop system are semi-globally, uniformly, and ultimately bounded. Simulation results demonstrate the effectiveness of the proposed controller.
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References
I. Kanellakopoulos, P. V. Kokotovic, and A. S. Morse, “Systematic design of adaptive controllers for feedback linearizable systems,” Proc. of American Control Conference, pp. 649–654, June 1991.
M. Chen, S. S. Ge, and B. V. E. How, “Robust adaptive neural network control for a class of uncertain mimo nonlinear systems with input nonlinearities,” IEEE Transactions on Neural Networks, vol. 21, no. 5, pp. 796–812, March 2010.
S. Sivrioglu, “Adaptive backstepping for switching control active magnetic bearing system with vibrating base,” IET Control Theory & Applications, vol. 1, no. 4, pp. 1054–1059, July 2007.
A. M. Zou, Z. G. Hou, and M. Tan, “Adaptive control of a class of nonlinear pure-feedback systems using fuzzy back-stepping approach,” IEEE Transactions on Fuzzy Systems, vol. 16, no. 4, pp. 886–897, August 2008.
S. Tong and Y. Li, “Robust adaptive fuzzy backstepping output feedback tracking control for nonlinear system with dynamic uncertainties,” Science China Information Sciences, vol. 53, no. 2, pp. 307–324, February 2010.
F. Wang, B. Chen, Y. Sun, Y. Gao, and C. Lin, “Finite-time fuzzy control of stochastic nonlinear systems,” IEEE Transactions on Cybernetics, vol. 50, no. 6, pp. 2617–2626, June 2019.
F. Wang and X. Zhang, “Adaptive finite time control of nonlinear systems under time-varying actuator failures,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 49, no. 9, pp. 1845–1852, September 2019.
L. B. Wu, and J. H. Park, “Adaptive fault-tolerant control of uncertain switched nonaffine nonlinear systems with actuator faults and time delays,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 50, no. 9 pp. 3470–3480, 2020.
L. B. Wu, J. H. Park, and N. N. Zhao, “Robust adaptive fault-tolerant tracking control for nonaffine stochastic nonlinear systems with full-state constraints,” IEEE Transactions on Cybernetics, vol 50, no. 8, pp. 3793–3805, 2020.
T. Sun, H. Pei, Y. Pan, H. Zhou, and C. Zhang, “Neural network-based sliding mode adaptive control for robot manipulators,” Neurocomputing, vol. 74, no. 14–15, pp. 2377–2384, July 2011.
T. Zhang, and S. S. Ge, “Adaptive neural control of mimo nonlinear state time-varying delay systems with unknown dead-zones and gain signs,” Automatica, vol. 43, no. 6, pp. 1021–1033, June 2007.
W. He, Y. Dong, and C. Sun, “Adaptive neural network control of unknown nonlinear affine systems with input deadzone and output constraint,” ISA Transactions, vol. 58, pp. 96–104, September 2015.
S. Zhou, M. Chen, C. J. Ong, and P. C. Chen, “Adaptive neural network control of uncertain mimo nonlinear systems with input saturation,” Neural Computing and Applications, vol. 27, no. 5, pp. 1317–1325, June 2016.
S. Tong and Y. Li, “Observer-based adaptive fuzzy back-stepping control of uncertain nonlinear pure-feedback systems,” Science China Information Sciences, vol. 57, pp. 1–14, Springer, May 2014.
Q. Zhou, C. Wu, and P. Shi, “Observer-based adaptive fuzzy tracking control of nonlinear systems with time delay and input saturation,” Fuzzy Sets and Systems, vol. 316, pp. 49–68, June 2017.
J. Kim, G. Caire, and A. F. Molisch, “Quality-aware streaming and scheduling for device-to-device video delivery,” IEEE/ACM Transactions on Networking, vol. 24, no. 4, pp. 2319–2331, August 2016.
C. Wu, J. Liu, Y. Xiong, and L. Wu, “Observer-based adaptive fault-tolerant tracking control of nonlinear nonstrict-feedback systems,” IEEE Transactions on Neural Networks and Learning Systems, vol. 29, no. 7, pp. 3022–3033, July 2017.
S. Tong, X. Min, and Y. Li, “Observer-based adaptive fuzzy tracking control for strict-feedback nonlinear systems with unknown control gain functions,” IEEE Transactions on Cybernetics, vol. 50, no. 9, pp. 3903–3913, 2020.
B. Chen, X. Liu, and C. Lin, “Observer and adaptive fuzzy control design for nonlinear strict-feedback systems with unknown virtual control coefficients,” IEEE Transactions on Fuzzy Systems, vol. 26, no. 3, pp. 1732–1743, June 2018.
C. P. Bechlioulis and G. A. Rovithakis, “Robust adaptive control of feedback linearizable mimo nonlinear systems with prescribed performance,” IEEE Transactions on Automatic Control, vol. 53, no. 9, pp. 2090–2099, October 2008.
A. Ilchmann, E. P. Ryan, and C. J. Sangwin, “Tracking with prescribed transient behaviour,” ESAIM: Control, Optimisation and Calculus of Variations, vol. 7, pp. 471–493, July 2002.
W. Sun, S. F. Su, G. Dong, and W. Bai, “Reduced adaptive fuzzy tracking control for high-order stochastic nonstrict feedback nonlinear system with full-state constraints,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019. DOI: https://doi.org/10.1109/TSMC.2019.2898204
C. Wang, Y. Wu, and J. Yu, “Barrier Lyapunov functions-based adaptive control for nonlinear pure-feedback systems with time-varying full state constraints,” International Journal of Control, Automation and Systems, vol. 15, no. 6, pp. 2714–2722, October 2017.
J. Zhang, “Integral barrier Lyapunov functions-based neural control for strict-feedback nonlinear systems with multi-constraint,” International Journal of Control, Automation and Systems, vol. 16, no. 4, pp. 2002–2010, July 2018.
J. X. Xu and X. Jin, “State-constrained iterative learning control for a class of MIMO systems,” IEEE Transactions on Automatic Control, vol. 58, no. 5, pp. 1322–1327, May 2013.
W. Sun, Y. Wu, and Z. Sun, “Command filter-based finite-time adaptive fuzzy control for uncertain nonlinear systems with prescribed performance,” IEEE Transactions on Fuzzy Systems, vol. 28, no. 12, pp. 311–3170, 2020.
J. X. Zhang and G. H. Yang, “Prescribed performance fault-tolerant control of uncertain nonlinear systems with unknown control directions,” IEEE Transactions on Automatic Control, vol. 62, no. 12, pp. 6529–6535, December 2017.
C. Liu, H. Wang, X. Liu, Y. Zhou, and S. Lu, “Adaptive prescribed performance tracking control for strict-feedback nonlinear systems with zero dynamics,” International Journal of Robust and Nonlinear Control, vol. 29, no. 18, pp. 6507–6521, October 2019.
W. Sun, F. S. Su, J. Xia, and G. Zhuang, “Command filter-based adaptive prescribed performance tracking control for stochastic uncertain nonlinear systems,” IEEE Transactions on Fuzzy Systems, 2020. DOI: https://doi.org/10.1109/TSMC.2019.2963220
C. Liu, H. Wang, X. Liu, and Y. Zhou, “Adaptive finite-time fuzzy funnel control for nonaffine nonlinear systems,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019. DOI: https://doi.org/10.1109/TSMC.2019.2917547
C. Liu, X. Liu, H. Wang, Y. Zhou, S. Lu, and B. Xu, “Event-triggered adaptive tracking control for uncertain nonlinear systems based on a new funnel function,” ISA Transactions, vol. 99, pp. 130–138, April 2020.
S. Tong and Y. Li, “Adaptive fuzzy output feedback control of mimo nonlinear systems with unknown dead-zone inputs,” IEEE Transactions on Fuzzy Systems, vol. 21, no. 1, pp. 134–146, February 2012.
W. Li, “Approaches to decision making with interval-valued intuitionistic fuzzy information and their application to enterprise financial performance assessment,” Journal of Intelligent & Fuzzy Systems, vol. 27, no. 1, pp. 1–8, February 2014.
T. P. Zhang and S. S. Ge, “Adaptive dynamic surface control of nonlinear systems with unknown dead zone in pure feedback form,” Automatica, vol. 44, no. 7, pp. 1895–1903, July 2008.
Y. J. Liu and S. Tong, “Adaptive NN tracking control of uncertain nonlinear discrete-time systems with nonaffine dead-zone input,” IEEE Transactions on Cybernetics, vol. 45, no. 3, pp. 497–505, March 2015.
J. Na, “Adaptive prescribed performance control of nonlinear systems with unknown dead zone,” International Journal of Adaptive Control and Signal Processing, vol. 27, no. 5, pp. 426–446, July 2012.
T. Zhang and S. S. Ge, “Adaptive neural control of mimo nonlinear state time-varying delay systems with unknown dead-zones and gain signs,” Automatica, vol. 43, no. 6, pp. 1021–1033, June 2007.
L. X. Wang, “Stable adaptive fuzzy control of nonlinear systems,” IEEE Transactions on Fuzzy Systems, vol. 1, no. 2, pp. 146–155, May 1993.
K. P. Tee, S. S. Ge, and E. H. Tay, “Barrier lyapunov functions for the control of output-constrained nonlinear systems,” Automatica, vol. 45, pp. 918–927, April, 2009.
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This work is supported in part by the Ministry of education industry-school cooperative education program (Grant No. 201901018003) and Excellent Talents Training Program of University of Science and Technology Liaoning (Grant No. 2019RC09).
Wen Zeng was born in Liaoning province, China in 1994, received his B.S. degree from University of Science and Technology Liaoning. Now he is a graduate student of control science and engineering in Liaoning University of Science and Technology, engaged in nonlinear system research.
Zhigang Li received his B.S. degree from Xi’an Jiaotong University, his M.S. degrees from Liaoning University of Technology. Now he is an associate professor and master’s supervisor of University of Science and Technology Liaoning. His research interests include artificial intelligence and pattern recognition.
Chuang Gao received his B.S. degree in Electronic and Communication Engineering from Warwick University, Coventry, UK, the M.S. degree in Digital Signal Processing from King’s College London, UK and a Ph.D. degree in Iron and Steel Metallurgy from University of Science and Technology Liaoning, Anshan, P. R. China, in 2005, 2007, and 2020, respectively. He has authored over 20 research papers indexed by SCI and EI. His research interests include nonlinear system control, machine learning and intelligent control.
Libing Wu received his B.S. and M.S. degrees from the Department of Mathematics, Jinzhou Normal College, Jinzhou, China, in 2004, and in Basic Mathematics from Northeastern University, Shenyang, China, in 2007, respectively, and a Ph.D. degree in Control Theory and Control Engineering from Northeastern University, Shenyang, China, in 2016. He is currently an Associate Professor at the School of Science, University of Science and Technology Liaoning, and also as a Postdoctoral Fellow at the Department of Electrical Engineering, Yeungnam University. His research interests include adaptive control, fault-tolerant control, nonlinear control and fault estimation.
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Zeng, W., Li, Z., Gao, C. et al. Observer-based Adaptive Fuzzy Control for Strict-feedback Nonlinear Systems with Prescribed Performance and Dead Zone. Int. J. Control Autom. Syst. 19, 1962–1975 (2021). https://doi.org/10.1007/s12555-020-0245-8
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DOI: https://doi.org/10.1007/s12555-020-0245-8