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Robust sliding mode control of general time-varying delay stochastic systems with structural uncertainties

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Abstract

This paper presents a new robust sliding mode control (SMC) method with well-developed theoretical proof for general uncertain time-varying delay stochastic systems with structural uncertainties and the Brownian noise (Wiener process). The key features of the proposed method are to apply singular value decomposition (SVD) to all structural uncertainties and to introduce adjustable parameters for control design along with the SMC method. It leads to a less-conservative condition for robust stability and a new robust controller for the general uncertain stochastic systems via linear matrix inequality (LMI) forms. The system states are able to reach the SMC switching surface as guaranteed in probability 1. Furthermore, it is theoretically proved that the proposed method with the SVD and adjustable parameters is less conservatism than the method without the SVD. The paper is mainly to provide all strict theoretical proofs for the method and results.

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Author information

Authors and Affiliations

  1. Department of Engineering Technology and Department of Software and Information Systems (Graduate Faculty), University of North Carolina at Charlotte (UNC Charlotte), Charlotte, NC, 28223-0001, USA

    Sheng-Guo Wang

  2. Department of Software and Information Systems, UNC Charlotte, Charlotte, NC, 28223-0001, USA

    Libin Bai

  3. College of Mathematics and Computer Science, Fuzhou University, Fuzhou Fujian, 350108, China

    Mingzhi Chen

Authors
  1. Sheng-Guo Wang
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  2. Libin Bai
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  3. Mingzhi Chen
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Corresponding author

Correspondence to Sheng-Guo Wang.

Additional information

This work was partially supported by the National Science Foundation Grants (Nos. 0940662, 1115564) of Prof. S.-G. Wang.

Sheng-Guo WANG received the B.Sc. and M.Sc. in Electrical Engineering from University of Science and Technology of China in 1967 and 1981, respectively, and the Ph.D. in Electrical & Computer Engineering from University of Houston in 1994.

He is a professor at University of North Carolina at Charlotte. He has published more than 100 papers in journals and conferences, and been the PI for numerous research projects since 1974. His research work has been supported by NSF, NCDOT, Tellabs, HP, Agilent, NASA, ARO, British Council, and China Railway. He is a frequent reviewer for more than 30 international journals and more than 10 international conferences. He has served as a program committee member (IPC) for more than 20 times, e.g., 2000 ACC; 2000 SPIE; 2005 BISBC; 2006 SICE-ICCAS; 2007 CBGI; 2007–2009, 2011 ISC; 2009 IEEE ISIC; 2010 IEEE CCA; 2012 ICEE; 2007, 2008, 2010- 2014 IEEE ICCAS, an invited session organizer for 2000 ACC, and more than 10 times as Session Chair/Co-chair for international conferences, e.g., IEEE CDC, WCICA, ACC and IFAC-WC. He has also served as an associate editor for JDSMC, JCTT, and IEEE MSC, etc. His current research interests include systems, control, circuits, modeling, robust control, GIS, big data, communications, computer networks, mathematical and numerical analysis, algorithms, applications.

Prof. Wang is a recipient of China National Science Conference Prize 1978 and many other academic awards, including the Best Session Paper Presentation Award of 2001 ACC, the inventor award for UNC Charlotte Invention 2001, an Outstanding Faculty Award at Prairie View A&M University 1997, Sigma Xi Research Excellence Award (UH Chapter) 1994, British Council Scholarship 1989. His membership includes IEEE, ASME, ASEE, Sigma Xi, and Tau Beta Pi.

Libin BAI received the B.Sc. degree in Electronic and Information Systems from Southwest University of Science and Technology, Mianyang, China in 2007, M.Sc. degree in Pattern Recognition and Intelligent Systems from University of Science and Technology of China, Hefei, China, in 2010, and Ph.D. degree in Software and Information Systems at University of North Carolina at Charlotte, U.S.A., in 2014. Currently, he is working at Marvell Semiconductor Inc. His current research interests include networked control systems, pattern recognition and GIS systems.

Mingzhi CHEN received the B.Sc. degree in Computer Networks from Fuzhou University, Fuzhou, China in 2003, M.Sc. degree in Computer Software and Theory, and Ph.D. degree in Communication and Information Systems from Fuzhou University, Fuzhou, China in 2005 and 2010, respectively.

He had been working at the University of North Carolina at Charlotte, U.S.A. as a postdoctoral fellow from August 2012 to September 2013. Currently, he is working at Fuzhou University as an associate professor. His current research interests include intelligent information processing and information security.

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Wang, SG., Bai, L. & Chen, M. Robust sliding mode control of general time-varying delay stochastic systems with structural uncertainties. Control Theory Technol. 12, 357–367 (2014). https://doi.org/10.1007/s11768-014-4055-5

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  • DOI: https://doi.org/10.1007/s11768-014-4055-5

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