Finite-Time Fuzzy Sliding Mode Control for Nonlinear Descriptor Systems

Zhixiong Zhong; Xingyi Wang; Hak-Keung Lam

doi:10.1109/JAS.2021.1004024

Volume 8 Issue 6

Jun. 2021

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2021 > 8(6): 1141-1152

Z. X. Zhong, X. Y. Wang, and H. Lam, "Finite-Time Fuzzy Sliding Mode Control for Nonlinear Descriptor Systems," IEEE/CAA J. Autom. Sinica, vol. 8, no. 6, pp. 1141-1152, Jun. 2021. doi: 10.1109/JAS.2021.1004024

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Z. X. Zhong, X. Y. Wang, and H. Lam, "Finite-Time Fuzzy Sliding Mode Control for Nonlinear Descriptor Systems," IEEE/CAA J. Autom. Sinica, vol. 8, no. 6, pp. 1141-1152, Jun. 2021. doi: 10.1109/JAS.2021.1004024

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Finite-Time Fuzzy Sliding Mode Control for Nonlinear Descriptor Systems

doi: 10.1109/JAS.2021.1004024

1.
Key Laboratory of Information Processing and Intelligent Control, Minjiang University, Fuzhou 350121, China
2.
College of Mechanical and Electronic Engineering, Fujian Agriculture and Forestry University, Fuzhou 350108, China
3.
Department of Engineering, King’s College London, London, WC2R 2LS, United Kingdom

Funds: This work was supported in part by the Central Government Drects Special Funds for Scientific and Technological Development of China (2019L3009), and Natural Science Foundation of Fujian Province of China (2020J02045)

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Author Bio:
Zhixiong Zhong (M’18) received the B.S. degree in mechatronics from Fuzhou University in 2008, and the M.S. degree in control theory and control engineering from Fuzhou University in 2012. In 2013 he was a visiting student with the Department of Mechanical Engineering, University of Victoria, Canada. In 2015 he received the Ph.D. degree in the Research Institute of Intelligent Control and Systems, Harbin Institute of Technology and jointed in the School of Computer and Control Engineering, Minjiang University in 2018. He is currently a Professor in Minjiang University. He has published more than 40 papers in journals, conferences, and authored two books: Modeling, Control, Estimation, and Optimization for Microgrids: A Fuzzy-Model-Based Method (CRC, 2019) and Large-Scale Fuzzy Interconnected Control Systems Design and Analysis (IGI Global, 2017). His research interests include fuzzy control, robust filtering, and large-scale control

Xingyi Wang received M.S. degree in control theory and control engineering from Fuzhou University in 2011. She is currently an Associate Professor in Minjiang University, and working toward the Ph.D. degree at the College of Mechanical and Electronic Engineering, Fujian Agriculture and Forestry University. Her research interests include fuzzy logic systems, control with neural networks

Hak-Keung Lam (M’98–SM’12–F’20) received the B.Eng. (Hons.) and Ph.D. degrees from the Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Hong Kong, China, in 1995 and 2000, respectively. During the period of 2000 and 2005, he worked with the Department of Electronic and Information Engineering at The Hong Kong Polytechnic University as Post-Doctoral Fellow and Research Fellow, respectively. He joined as a Lecturer at King’s College London in 2005 and is currently a Reader. His current research interests include intelligent control systems and computational intelligence. He has served as a program committee member and international advisory board member for various international conferences and a reviewer for various books, international journals and international conferences. He is an Associate Editor for IEEE Transactions on Fuzzy Systems, IEEE Transactions on Circuits and Systems II: Express Briefs, IET Control Theory and Applications, International Journal of Fuzzy Systems, Neurocomputing, and Nonlinear Dynamics; and Guest Editor for a number of international journals, and is in the editorial board of for a number of international journals. He was named as Highly Cited Researcher and is an IEEE Fellow. He is the coeditor for two edited volumes: Control of Chaotic Nonlinear Circuits (World Scientific, 2009) and Computational Intelligence and Its Applications (World Scientific, 2012), and the coauthor of the monographs: Stability Analysis of Fuzzy-Model-Based Control Systems (Springer, 2011), Polynomial Fuzzy Model Based Control Systems (Springer, 2016), and Analysis and Synthesis for Interval Type-2 Fuzzy-Model-Based Systems (Springer, 2016)
Corresponding author: Xingyi Wang, e-mail: xingyiwang2019@126.com
Received Date: 2020-02-05
Revised Date: 2021-01-10
Accepted Date: 2021-03-14

Available Online: 2021-03-26

Abstract

Abstract

This article addresses the finite-time boundedness (FTB) problem for nonlinear descriptor systems. Firstly, the nonlinear descriptor system is represented by the Takagi-Sugeno (T-S) model, where fuzzy representation is assumed to be appearing not only in both the state and input matrices but also in the derivative matrix. By using a descriptor redundancy approach, the fuzzy representation in the derivative matrix is reformulated into a linear one. Then, we introduce a fuzzy sliding mode control (FSMC) law, which ensures the finite-time boundedness (FTB) of closed-loop fuzzy control systems over the reaching phase and sliding motion phase. Moreover, by further employing the descriptor redundancy representation, the sufficient condition for designing FSMC law, which ensures the FTB of the closed-loop control systems over the entire finite-time interval, is derived in terms of linear matrix inequalities (LMIs). Finally, a simulation study with control of a photovoltaic (PV) nonlinear system is given to show the effectiveness of the proposed method.
- Finite-time boundedness (FTB),
- fuzzy sliding mode control (FSMC),
- Takagi-Sugeno (T-S) fuzzy descriptor system

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References

[1]	J. Garibaldi, “The need for fuzzy AI,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 3, pp. 610–622, 2019. doi: 10.1109/JAS.2019.1911465
[2]	W. He, L. Kong, Y. Dong, Y. Yu, C. Yang, and C. Sun, “Fuzzy tracking control for a class of uncertain MIMO nonlinear systems with state constraints,” IEEE Trans. Systems,Man,and Cybernetics:Systems, vol. 49, no. 3, pp. 543–554, 2019. doi: 10.1109/TSMC.2017.2749124
[3]	Z. Zhang, H. Li, C. Wu, and Qi Zhou, “Finite frequency fuzzy H_∞ control for uncertain active suspension systems with sensor failure,” IEEE/CAA J. Autom. Sinica, vol. 5, no. 4, pp. 777–786, 2018. doi: 10.1109/JAS.2018.7511132
[4]	T. Haidegger, L. Kovacs, S. Preitl, R. Precup, B. Benyo, and Z. Benyo, “Controller design solutions for long distance telesurgical applications,” Int. J. Artificial Intelligence, vol. 6, no. S11, pp. 48–71, 2011.
[5]	A. Takacs, L. Kovacs, I. Rudas, R. Precup, and T. Haidegger, “Models for force control in telesurgical robot systems,” Acta Polytechnica Hungarica, vol. 12, no. 8, pp. 95–114, 2015.
[6]	L. Kong, W. He, C. Yang, Z. Li, and C. Sun, “Adaptive fuzzy control for coordinated multiple robots with constraint using impedance learning,” IEEE Trans. Cybernetics, vol. 49, no. 8, pp. 3052–3063, 2019. doi: 10.1109/TCYB.2018.2838573
[7]	S. Sun, H. Zhang, Z. Qin, and R. Xi, “Delay-dependent H_∞ guaranteed cost control for uncertain switched T-S fuzzy systems with multiple interval time-varying delays,” IEEE Trans. Fuzzy Systems, 2020. DOI: 10.1109/TFUZZ.2020.2968877
[8]	X. Zhao, L. Zhang, P. Shi, and H. Karimi, “Novel stability criteria for T-S fuzzy systems,” IEEE Trans. Fuzzy Systems, vol. 22, no. 2, pp. 313–323, 2014. doi: 10.1109/TFUZZ.2013.2254491
[9]	Z. Zhong, Y. Zhu, M.V. Basin, and H.K. Lam, “Event-based multirate control of large-scale distributed nonlinear systems subject to time-driven zero order holds,” Nonlinear Analysis:Hybrid Systems, vol. 36, no. 100864, pp. 1–18, 2020.
[10]	W. He, X. Mu, L. Zhang, and Y. Zou, “Modeling and trajectory tracking control for flapping-wing micro aerial vehicles,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 1, pp. 148–156, Jan. 2021. doi: 10.1109/JAS.2020.1003417
[11]	H. Gao, W. He, L. Zhang, and C. Sun, “Neural-network control of a stand-alone tall building-like structure with an eccentric load: An experimental investigation,” IEEE Trans. Cybernetics, 2020. DOI: 10.1109/TCYB.2020.3006206
[12]	M. Basin, “Applying sliding mode technique to optimal filter and controller design,” Lecture Notes in Control &Information Sciences, vol. 412, pp. 325–349, 2011.
[13]	H. Karimi, “A sliding mode approach to H_∞ synchronization of master-slave time-delay systems with Markovian jumping parameters and nonlinear uncertainties,” Journal of the Franklin Institute, vol. 349, no. 4, pp. 1480–1496, 2012. doi: 10.1016/j.jfranklin.2011.09.015
[14]	G. Liu, S. Xu, Y. Wei, Z. Qi, and Z. Zhang, “New insight into reachable set estimation for uncertain singular time-delay systems,” Applied Mathematics and Computation, vol. 320, pp. 769–780, 2018. doi: 10.1016/j.amc.2017.10.035
[15]	J. Li, Q. Zhang, X. Yan, and S. Spurgeon, “Observer-based fuzzy integral sliding mode control for nonlinear descriptor systems,” IEEE Trans. Fuzzy Systems, vol. 26, no. 5, pp. 2818–2832, 2018. doi: 10.1109/TFUZZ.2018.2802458
[16]	Y. Wang, H. Karimi, H. Shen, Z. Fang, and M. Liu, “Fuzzy-model-based sliding mode control of nonlinear descriptor systems,” IEEE Trans. Cybernetics, vol. 49, no. 9, pp. 3409–3419, 2018.
[17]	Y. Wang, J. Zhang, H. Zhang, and J. Sun, “A new stochastic sliding-mode design for descriptor fuzzy systems with time-varying delay,” IEEE Trans. Cybernetics, 2019. DOI: 10.1109/TCYB.2019.2945795
[18]	C. Yang, Y. Jiang, J. Na, Z. Li, L. Cheng, and C. Su, “Finite-time convergence adaptive fuzzy control for dual-arm robot with unknown kinematics and dynamics,” IEEE Trans. Fuzzy Systems, vol. 27, no. 3, pp. 574–588, 2019. doi: 10.1109/TFUZZ.2018.2864940
[19]	C. Yang, Y. Jiang, W. He, J. Na, Z. Li, and B. Xu, “Adaptive parameter estimation and control design for robot manipulators with finite-time convergence,” IEEE Trans. Industrial Electronics, vol. 65, no. 10, pp. 8112–8123, 2018. doi: 10.1109/TIE.2018.2803773
[20]	X. Lin, S. Huang, W. Zhang, and S. Li, “Finite-time feedback stabilization of a class of input-delay systems with saturating actuators via digital control,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 5, pp. 1281–1290, 2019. doi: 10.1109/JAS.2019.1911525
[21]	Z. Cao, Y. Niu, and J. Song, “Finite-time sliding mode control of Markovian jump cyber-physical systems against randomly occurring injection attacks,” IEEE Trans. Automatic Control, vol. 65, no. 3, pp. 1264–1271, 2020. doi: 10.1109/TAC.2019.2926156
[22]	Y. Li, K. Li, and S. Tong, “Finite-time adaptive fuzzy output feedback dynamic surface control for MIMO nonstrict feedback systems,” IEEE Trans. Fuzzy Systems, vol. 27, no. 1, pp. 96–110, 2019. doi: 10.1109/TFUZZ.2018.2868898
[23]	Y. Li, K. Li, and S. Tong, “Adaptive Neural network finite-time control for multi-input and multi-output nonlinear systems with positive powers of odd rational numbers,” IEEE Trans. Neural Networks and Learning Systems, vol. 31, no. 7, pp. 2532–2543, 2020.
[24]	Z. Zhong, Y. Zhu, C. Lin, and T. Huang, “A fuzzy control framework for interconnected nonlinear power networks under TDS attack: Estimation and compensation,” Journal of the Franklin Institute, vol. 358, no. 1, pp. 74–88, 2021. doi: 10.1016/j.jfranklin.2018.12.012
[25]	Z. Su, Q. Zhang, and J. Ai, “Practical and finite-time fuzzy adaptive control for nonlinear descriptor systems with uncertainties of unknown bound,” Int. J. Systems Science, vol. 44, no. 12, pp. 2223–2233, 2013. doi: 10.1080/00207721.2012.687784
[26]	M. Basin, “Finite- and fixed-time convergent algorithms: Design and convergence time estimation,” Annual Reviews in Control, vol. 48, pp. 209–221, 2019. doi: 10.1016/j.arcontrol.2019.05.007
[27]	T. Taniguchi, K. Tanaka, and H. Wang, “Fuzzy descriptor systems and nonlinear model following control,” IEEE Trans. Fuzzy Systems, vol. 8, no. 4, pp. 442–452, 2000. doi: 10.1109/91.868950
[28]	R. Kavikumar, R. Sakthivel, O.M. Kwon, and B. Kaviarasan, “Finite-time boundedness of interval type-2 fuzzy systems with time delay and actuator faults R,” Journal of the Franklin Institute, vol. 356, pp. 8296–8324, 2019. doi: 10.1016/j.jfranklin.2019.07.031
[29]	H. Shen, F. Li, H. Yan, H. Karimi, and H. Lam, “Finite-time event-triggered H_∞ control for T-S fuzzy markov jump systems,” IEEE Trans. Fuzzy Systems, vol. 26, no. 5, pp. 3122–3135, 2018. doi: 10.1109/TFUZZ.2017.2788891
[30]	Z. Xiang, C. Qiao, and M. Mahmoud, “Finite-time analysis and H_∞ control for switched stochastic systems,” Journal of the Franklin Institute, vol. 349, no. 3, pp. 915–927, 2012. doi: 10.1016/j.jfranklin.2011.10.021
[31]	B. Xiao, Q. Hu, and Y. Zhang, “Finite-time attitude tracking of spacecraft with fault-tolerant capability,” IEEE Trans. Control Systems Technology, vol. 23, no. 4, pp. 1338–1350, 2015. doi: 10.1109/TCST.2014.2364124
[32]	S. Huang, Z. Xiang, and H. Karimi, “Input-output finite-time stability of discrete-time impulsive switched linear systems with state delays,” Circuits Systems &Signal Processing, vol. 33, no. 1, pp. 141–158, 2014.
[33]	J. Song, Y. Niu, and Y. Zou, “Finite-time stabilization via sliding mode control,” IEEE Trans. Automatic Control, vol. 62, no. 3, pp. 1478–1483, 2017. doi: 10.1109/TAC.2016.2578300
[34]	W. Haddad and A. L’Afflitto, “Finite-time stabilization and optimal feedback control,” IEEE Trans. Automatic Control, vol. 61, no. 4, pp. 1069–1074, 2016. doi: 10.1109/TAC.2015.2454891
[35]	M. Chadli and H. Karimi, “Robust observer design for unknown inputs Takagi-Sugeno models,” IEEE Trans. Fuzzy Systems, vol. 21, no. 1, pp. 158–164, 2013. doi: 10.1109/TFUZZ.2012.2197215
[36]	K. Tanaka, H. Ohtake, and H. Wang, “A descriptor system approach to fuzzy control system design via fuzzy Lyapunov functions,” IEEE Trans. Fuzzy Systems, vol. 15, no. 3, pp. 333–341, 2007. doi: 10.1109/TFUZZ.2006.880005
[37]	Z. Zhong, C. Lin, Z. Shao, and M. Xu, “Decentralized event-triggered control for large-scale networked fuzzy systems,” IEEE Trans. Fuzzy Systems, vol. 26, no. 1, pp. 29–45, 2018. doi: 10.1109/TFUZZ.2016.2634090

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By using a descriptor redundancy approach, the fuzzy representation in the derivative matrix of system is reformulated into the linear one.
For a specified time interval, partition with transient dynamics of sliding mode control into two subintervals: Reaching phase and sliding motion phase.
Based on the Lyapunov function in the descriptor system domain, the design of FSMC Law is derived in terms of LMIs.

Finite-Time Fuzzy Sliding Mode Control for Nonlinear Descriptor Systems

doi: 10.1109/JAS.2021.1004024

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