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Observer-based Sliding Mode Control for Fractional Order Singular Fuzzy Systems

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  • Control Theory and Applications
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Abstract

In the paper, observer-based sliding mode control (SMC) for fractional order singular fuzzy (FOSF) systems with order 0 < α < 1 is studied. The non-fragile FOSF observer is designed to reconstruct the unmeasured states, and a novel fractional order integral sliding function is formulated. Then, the admissibility condition of the FOSF error system is derived, based on the linear matrix inequality (LMI) approach. By using the singular value decomposition approach, the strict LMI-based admissibility condition is improved. Based on the fractional order Lyapunov function and sliding surface, the fractional order SMC is constructed to ensure the reachability of the sliding surface. Two examples are given to illustrate the effectiveness of the methods proposed in the paper.

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Authors and Affiliations

  1. Institute of Robotics and Automatic Information System (IRAIS) and the Tianjin Key Laboratory of Intelligent Robotic (tjKLIR), Nankai University, Tianjin, 300350, China

    Bingxin Li, Xiangfei Zhao, Yaowei Liu & Xin Zhao

  2. Institute of Intelligence Technology and Robotic Systems, Shenzhen Research Institute of Nankai University, Shenzhen, 518083, China

    Bingxin Li, Xiangfei Zhao, Yaowei Liu & Xin Zhao

  3. College of Sciences, Northeastern University, Shenyang, Liaoning, 110819, China

    Xuefeng Zhang

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  1. Bingxin Li
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  5. Xin Zhao
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Correspondence to Xin Zhao.

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This research was jointly supported by National Natural Science Foundation of China (62027812, 62273185, 62273186).

Bingxin Li received his B.S. degree in automation from Shandong University, Jinan, China, in 2014, an M.S. degree in systems analysis and integration from Northeastern University, Shenyang, China, in 2017, and he is currently pursuing a Ph.D. degree in control science and engineering from Nankai University. His research interests include fractional order control systems, singular systems, and robust control.

Xuefeng Zhang received his B.Sc. degree in applied mathematics, an M.S. degree in control theory and control engineering, and a Ph.D. degree in control theory and control engineering from Northeastern University, Shenyang, China, in 1989, 2004, and 2008, respectively, where he is currently with the college of Sciences. He has published more than 100 journal and conference papers and 3 books. He is the Associate Editor of IEEE Access and the Committee member of Technical Committee on Fractional and Control of Chinese Association of Automation. His research interests include fractional order control systems and singular systems.

Xiangfei Zhao received his B.S. degree from Department of Wind Energy and Power Engineering, Hebei University of Technology, Tianjin, China, in 2013, an M.A. degree from the Automation College of Tianjin University of Technology, Tianjin, China, in 2017. He is currently working toward a Ph.D. degree in control theory and control engineering with the Nankai University, Tianjin, China. His current research interests include micromanipulation and microsystems.

Yaowei Liu received his B.Eng. degree in automation and a Ph.D. degree in control theory and control engineering from Nankai University, Tianjin, China, in 2013 and 2019, respectively. He is currently a Post-Doctoral Fellow with the College of Artificial Intelligence, Nankai University, Tianjin, China. He is also with Institute of Intelligence Technology and Robotic Systems, Shenzhen Research Institute of Nankai University, Shenzhen, China. His research interests include micromanipulators and microsystems.

Xin Zhao received his B.S. degree in control theory and control engineering from Nankai University, Tianjin, China, in 1991, an M.S. degree in control theory and control engineering from the Shenyang Institute of Automation, CAS, Shenyang, China, in 1994, and a Ph.D. degree in control theory and control engineering from Nankai University in 1997. He joined the faculty at Nankai University in 1997, where he is currently a Professor and the Dean of the College of Artificial Intelligence. His current research interests include micromanipulator, microsystems, and mathematical biology.

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Li, B., Zhang, X., Zhao, X. et al. Observer-based Sliding Mode Control for Fractional Order Singular Fuzzy Systems. Int. J. Control Autom. Syst. 21, 2879–2890 (2023). https://doi.org/10.1007/s12555-022-0396-x

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