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

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• 作者：Sheng-Guo Wang (1)
  Libin Bai (2)
  Mingzhi Chen (3)
  
  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
  2. Department of Software and Information Systems ; UNC Charlotte ; Charlotte ; NC ; 28223-0001 ; USA
  3. College of Mathematics and Computer Science ; Fuzhou University ; Fuzhou Fujian ; 350108 ; China
  
• 关键词：Robust control ; Time ; varying delay systems ; Stochastic systems ; Lyapunov methods ; Sliding mode control ; Time ; varying systems
• 刊名：Journal of Control Theory and Applications
• 出版年：2014
• 出版时间：November 2014
• 年：2014
• 卷：12
• 期：4
• 页码：357-367
• 全文大小：403 KB
• 参考文献：1. J. Chiasson, J. J. Loisean. Application of Time Delay Systems. 1st ed. London: Springer, 2007. CrossRef
  2. P. F. Hokayem, M. W. Spong. Bilateral teleoperation: an historical survey. Automatica, 2006, 42(12): 2035鈥?057. CrossRef
  3. A. D. Zeitlin, M. P. McLaughlin. Safety of cooperative collision avoidance for unmanned aircraft. Proceedings of the 25th Digital Avionics Systems Conference. Piscataway: IEEE, 2006: 868鈥?74.
  4. J. Kaloust, C. Ham, J. Siehling. Nonlinear robust control design for levitation and propulsion of a maglev system. IEE Proceedings-Control Theory and Applications, 2004, 151(4): 460鈥?64. CrossRef
  5. R. Brooks. A robust layered control system for a mobile robot. IEEE Journal of Robotics and Automation, 1986, 2(1): 14鈥?3. CrossRef
  6. T. Umeno, Y. Hori. Robust speed control of DC servomotors using modern two degrees-of-freedom controller design. IEEE Transactions on Industrial Electronics, 1991, 38(5): 363鈥?68. CrossRef
  7. P. Shi, G. Liu, D. Rees, et al. Active disturbance rejection control for uncertain multivariable systems with time-delay. IET Control Theory & Applications, 2007, 1(1): 75鈥?1. CrossRef
  8. B. Du, J. Lam, Y. Zou, et al. Stability and stabilization for Markovian jump time-delay systems with partially unknown transition rates. IEEE Transactions on Circuits and Systems 鈥?I: Regular Papers, 2013, 60(2): 341鈥?51. CrossRef
  9. M. Y. Chow, Y. Tipsuwan. Network-based control systems: a tutorial. Proceedings of the 27th Annual Conference of the IEEE Industrial Electronics Society. Piscataway: IEEE, 2001: 1593鈥?602.
  10. E. Fridman, U. Shaked. Special issue on time-delay systems. International Journal of Robust and Nonlinear Control, 2003, 13(9): 791鈥?92. CrossRef
  11. Y. Liu, B. Xu, B. Shi. Kalman filtering for stochastic systems with consecutive packet losses and measurement time delays. Control Theory & Applications, 2013, 30(7): 898鈥?08.
  12. Y. Fu, Z. Tian, S. Shi. Output feedback stabilization for stochastic time-delay nonlinear systems. Control Theory & Applications, 2003, 20(5): 749鈥?52.
  13. Q. Wang, R. F. Stengel. Robust nonlinear control of a hypersonic aircraft. Journal of Guidance, Control, and Dynamics, 2000, 23(4): 577鈥?85. CrossRef
  14. A. Kuperman, Q. C. Zhong. Robust control of uncertain nonlinear systems with state delays based on an uncertainty and disturbance estimator. International Journal of Robust and Nonlinear Control, 2011, 21(1): 79鈥?2. CrossRef
  15. S. Xu, P. Shi, Y. Chu. Robust stochastic stabilization and H<sub>鈭?/sub> control of uncertain neutral stochastic time-delay systems. Journal of Mathematical Analysis and Applications, 2006, 314(1): 1鈥?6. CrossRef
  16. P. Shi, X. Luan, F. Liu. H鈭?/sub> filtering for discrete-time systems with stochastic incomplete measurement and mixed delays. IEEE Transactions on Industrial Electronics, 2012, 59(6): 2732鈥?739. CrossRef
  17. V. I. Utkin. Sliding mode control design principles and applications to electric drives. IEEE Transactions on Industrial Electronics, 1993, 40(1): 23鈥?6. CrossRef
  18. Y. H. Roh, J. H. Oh. Robust stabilization of uncertain inputdelay systems by sliding mode control with delay compensation. Automatica, 1999, 35(11): 1861鈥?865. CrossRef
  19. Y. Xia, Y. Jia. Robust sliding-mode control for uncertain time-delay systems: an LMI approach. IEEE Transactions on Automatic Control, 2003, 48(6): 1086鈥?091. CrossRef
  20. M. Liu, P. Shi, L. Zhang, et al. Fault-tolerant control for nonlinear Markovian jump systems via proportional and derivative sliding mode observer technique. IEEE Transactions on Circuits and Systems 鈥?I, 2011, 58(11): 2755鈥?764. CrossRef
  21. Y. Niu, D. Ho, J. Lam. Robust integral sliding mode control for uncertain stochastic systems with time-varying delay. Automatica, 2005, 41(5): 873鈥?80. CrossRef
  22. L. Yu, J. Chu. An LMI approach to guaranteed cost control of linear uncertain time-delay systems. Automatica, 1999, 35(6): 1155鈥?159. CrossRef
  23. C. E. de Souze, X. Li. Delay-dependent robust H鈭?/sub> control of uncertain linear state-delayed systems. Automatica, 1999, 35(7): 1313鈥?321. CrossRef
  24. L. Wu, X. Su, P. Shi. Sliding mode control with bounded / L 2 gain performance of Markovian jump singular time-delay systems. Automatica, 2012, 48(8): 1929鈥?933. CrossRef
  25. S. Wang, H. Y. Yeh, P. Roschke. Robust control for structural systems with parametric and unstructured uncertainties. Journal of Vibration and Control, 2001, 7(5): 753鈥?72. CrossRef
  26. S. Wang, L. S. Shieh, J. W. Sunkel. Robust optimal pole-placement in a vertical strip and disturbance rejection. Proceedings of the 32nd IEEE Conference on Decision and Control. San Antonio: IEEE, 1993: 1134鈥?139.
  27. S. Wang, S. Lin, L. S. Shieh, et al. Observer based controller for robust pole clustering in a vertical strip and disturbance rejection in structured uncertain systems. International Journal of Robust and Nonlinear Control, 1998, 8(12): 1073鈥?084. CrossRef
  28. K. Zhou, P. P. Khargonekar, J. Stousrup, et al. Robust performance of systems with structured uncertainties in state space. Automatica, 1995, 31(2): 249鈥?55. CrossRef
  29. S. Wang, L. Bai. Flexible robust sliding mode control for uncertain stochastic systems with time-varying delay and structural uncertainties. Proceedings of the 51st IEEE Annual Conference on Decision and Control. New York: IEEE, 2012: 1536鈥?541.
  30. S. Xu, T. Chen. Robust H鈭?/sub> control for uncertain stochastic systems with state delay. IEEE Transactions on Automatic Control, 2002, 47(12): 2089鈥?094. CrossRef
  31. I. Schur. 脺ber Potenzreihen, die im Innern des Einheitskreises beschr盲nkt sind. Journal f眉r die reine und angewandte Mathematik, 1917, 1917(147): 205鈥?32.
  32. S. Wang. Robust active control for uncertain structural systems with acceleration sensors. Journal of Structural Control, 2003, 10(1): 59鈥?6. CrossRef
  33. L. Xie, M. Fu, C. E. de Souza. H鈭?/sub> control and quadratic stabilization of systems with parameter uncertainty via output feedback. IEEE Transactions on Automatica Control, 1992, 37(8): 1253鈥?256. CrossRef
  34. P. Gahinet, A. Nemirovski, A. J. Laub, et al. LMI Control Toolbox. 1995: http://www.mathworks.de/help/releases/R13sp2/pdf_doc/lmi/lmi.pdf.
  35. S. Wang. New Lyapunov-type Functional for General Stochastic Systems with Time-varying Delay. Technical note. Charlotte: UNC Charlotte, 2013.</sub>
  
• 刊物类别：Computer Science
• 刊物主题：Control Structures and Microprogramming
  Chinese Library of Science
  
• 出版者：South China University of Technology and Academy of Mathematics and Systems Science, CAS
• ISSN：1993-0623

文摘

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.