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Intelligent Digital Redesign for Sampled-data Fuzzy Control Systems Based on State-matching Error Cost Function Approach

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  • Intelligent Control and Applications
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Abstract

This paper presents a novel intelligent digital redesign (IDR) technique for a sampled-data fuzzy controller of fuzzy systems which can be modeled in Takagi-Sugeno (T-S) fuzzy systems. The IDR technique, which is one of sampled-data fuzzy controller design techniques, is to effectively convert a well-designed analog fuzzy controller into a sampled-data fuzzy controller in the state-matching sense. In this paper, unlike previous IDR techniques, the state-matching error is minimized by defining the state-matching error cost function. Also, to improve the state-matching condition, the exact discretized model is used for the proposed IDR technique. The sufficient condition of the proposed IDR technique is developed and derived in terms of linear matrix inequalities (LMIs). Finally, some numerical examples are provided to verify the effectiveness of the proposed techniques.

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References

  1. D. Nešić and A. R. Teel, “Sampled-data control of nonlinear systems: an overview of recent results,” Perspectives in Robust Control, vol. 268, pp. 221–239, 2001. [click]

    Article  MathSciNet  MATH  Google Scholar 

  2. L. S. Hu, T. Bai, P. Shi, and Z. Wu, “Sampled-data control of networked linear control systems,” Automatica, vol. 43, pp 903–911, 2007. [click]

    Article  MathSciNet  MATH  Google Scholar 

  3. H. K. Lam and L. D. Seneviratne, “Tracking control of sampled-data fuzzy-model-based control systems,” IET Control Theory Appl., vol. 13, no. 1, pp. 56–67, 2009.

    Article  MathSciNet  Google Scholar 

  4. B. C. Kuo, Digital Control Systems, Holt, Rinehart and Winston, New York, 1980.

    Google Scholar 

  5. T. Chen and B. Francis, Optimal Sampled-data Control Systems, Springer, London, 1995.

    Book  MATH  Google Scholar 

  6. P. Dorato, C. Abdallah, and V. Cerone, Linear-Quadaratic Control: An Introduction, Prentice-Hall, New Jersey, 1995.

    MATH  Google Scholar 

  7. L. S. Shieh, W. M. Wang, and J. S. H. Tsai, “Digital modelling and digital redesign of sampled-data uncertain systems”, IEE Proc. Control Theory Appl., vol. 142, no. 6, pp. 585–594, 1995. [click]

    Article  MATH  Google Scholar 

  8. L. S. Shieh, W. M. Wang, and J. B. Zheng, “Robust control of sampled-data uncertain systems using digitally redesigned observer-based controllers,” Int. J. Control, vol. 66, pp. 43–64, 1997. [click]

    Article  MathSciNet  MATH  Google Scholar 

  9. C. A. Rabbath, N. Hori, and N. Lechevin, “Convergence of sampled-data models in digital redesign,” IEEE Trans. Autom. Control, vol. 49, no. 5, pp. 850–855, 2004. [click]

    Article  MathSciNet  MATH  Google Scholar 

  10. S. M. Guo, L. S. Shieh, G. Chen, and C. F. Lin, “Effective chaotic orbit tracker: a prediction-based digital redesign approach,” IEEE Trans. Circ. Syst. I, vol. 47, no. 11, pp. 1557–1570, 2000. [click]

    Article  MathSciNet  MATH  Google Scholar 

  11. J. S. H. Tsai, L. S. Shieh, and J. L. Zhang, “An improvement on the digital redesign method based on the blockpulse function approximation,” Circuits Syst. Signal Process., vol. 12, no. 1, pp. 37–49, 1993.

    Article  MATH  Google Scholar 

  12. Y. N. Rosenwasser, K. Y. Polyakov, and B. P. Lampe, “Application of Laplace transformation for digital redesign of continuous control systems,” IEEE Trans. Autom. Control, vol. 44, no. 4, pp. 883–886, 1999. [click]

    Article  MathSciNet  MATH  Google Scholar 

  13. E. N. Rosenwasser and B.P. Lampe, Computer Controlled Systems -Analysis and Design with Process-Orientated Models, Springer, London, 2000.

    MATH  Google Scholar 

  14. S. M. Guo and Z. H. Peng, “An observer-based decentralized tracker for sampled-data systems: An evolutionary programming approach,” Int. J. General Syst., vol. 34, no. 4, pp. 421–449, 2005. [click]

    Article  MathSciNet  MATH  Google Scholar 

  15. C. C. Hsu and G. Y. Lin, “Digital redesign of uncertain interval systems based on time-response resemblance via particle swarm optimization,” ISA Trans., vol. 48, pp. 264–272, 2009.

    Article  Google Scholar 

  16. C. C. Hsu, W. Y. Shieh, and C. H. Gao, “Digital redesign of uncertain interval systems based on extremal gain/phase margins via a hybrid particle swarm optimizer,” Appl. Soft Comput., vol. 10, no. 2, pp. 602–612, 2010. [click]

    Article  Google Scholar 

  17. H. J. Lee, L. S. Shieh, and D. W. Kim, “Digital control of nonlinear systems: Optimal linearisation-based digital redesign approach,” IET Control Theory Appl., vol. 2, no. 4, pp. 337–351, 2008. [click]

    Article  MathSciNet  Google Scholar 

  18. D. W. Kim and H. J. Lee, “Controlling linear systems with nonlinear perturbations under sampled-data output feedback: Digital redesign approach,” Int. J. Control, vol. 83, no. 8, pp. 1718–1726, 2010. [click]

    Article  MathSciNet  MATH  Google Scholar 

  19. D. H. Lee, Y. H. Joo, and S. K. Kim, “H ∞ digital redesign for LTI systems,” Int. J. Control, Autom. Syst., vol. 13, no. 3, pp. 603–610, 2015. [click]

    Article  Google Scholar 

  20. Y. H. Joo, G. Chen, and L. S. Shieh, “Hybrid state-space fuzzy model-based controller with dual-rate sampling for digital control of chaotic sysems,” IEEE Trans. Fuzzy Syst., vol. 7, no. 4, pp. 394–408, 1999. [click]

    Article  Google Scholar 

  21. H. J. Lee, H. B. Kim, Y. H. Joo, W. Chang, and J. B. Park, “A new intelligent digital redesign for T-S fuzzy systems: global approach,” IEEE Trans. Fuzzy Syst., vol. 12, no. 2, pp. 274–284, 2004. [click]

    Article  Google Scholar 

  22. H. C. Sung, D. W. Kim, J. B. Park, and Y.H. Joo, “Robust digital control of fuzzy systems with parametric uncertainties: LMI-based digital redesign approach,” Fuzzy Sets Syst., vol. 161, pp. 919–933, 2010. [click]

    Article  MathSciNet  MATH  Google Scholar 

  23. G. B. Koo, J. B. Park, and Y. H. Joo, “Intelligent digital redesign for nonlinear systems using a guaranteed cost control method,” Int. J. Control, Autom. Syst., vol. 11, no. 6, pp. 1075–1083, 2013. [click]

    Article  Google Scholar 

  24. J. H. Moon and H. J. Lee, “Performance recovery of intelligent digital redesign for observer-based output feedback under immeasurable premise variables,” IET Control Theory Appl., vol. 9, no. 12, pp. 1846–1856, 2015. [click]

    Article  MathSciNet  Google Scholar 

  25. G. B. Koo, J. B. Park, and Y. H. Joo, “Intelligent digital redesign for non-linear systems: observer-based sampleddata fuzzy control approach,” IET Control Theory Appl., vol. 10, no. 1, pp. 1–9, 2016.

    Article  MathSciNet  Google Scholar 

  26. G. B. Koo, J. B. Park, and Y. H. Joo, “Intelligent digital redesign of fuzzy controller for non-linear systems with packet losses,” IET Control Theory Appl., vol. 10, no. 3, pp. 292–299, 2016. [click]

    Article  MathSciNet  Google Scholar 

  27. H. J. Lee and D.W. Kim, “Performance-recoverable intelligent digital redesign for fuzzy tracking controllers,” Infom. Sci., vol. 10, no. 3, pp. 292–299, 2016.

    Google Scholar 

  28. S. C. Jee, H. J. Lee, and D. W. Kim, “Detecting sensor fault for nonlinear systems in T-S form under sampled-data measurement: Exact direct discrete-time design approach,” Int. J. Control, Autom. Syst., vol. 14, no. 2, pp. 435–442, 2016.

    Article  Google Scholar 

  29. H. J. Kim, J. B. Park, and Y. H. Joo, “Fuzzy filter for nonlinear sampled-data systems: intelligent digital redesign approach,” Int. J. Control, Autom. Syst., vol. 15, no. 2, pp. 603–610, 2017. [click]

    Article  Google Scholar 

  30. H. J. Kim, J. B. Park, and Y. H. Joo, “An improved H ∞ fuzzyy filter for nonlinear sampled-data systems,” Int. J. Control, Autom. Syst., vol. 15, no. 3, pp. 1394–1404, 2017. [click]

    Article  Google Scholar 

  31. D. W. Kim, H. J. Lee, and M. Tomizuka, “Fuzzy stabilization of nonlinear systems under sampled-data feedback: an exact discrete-time model approach,” IEEE Trans. Fuzzy Syst., vol. 18, no. 2, pp. 251–260, 2010. [click]

    Google Scholar 

  32. D. W. Kim and H. J. Lee, “Sampled-data observer-based output-feedback fuzzy stabilization of nonlinear systems: exact discrete-time design approach,” Fuzzy Sets Syst., vol. 201, pp. 20–39, 2012. [click]

    Article  MathSciNet  MATH  Google Scholar 

  33. K. Gu, “An integral inequality in the stability problem of time-delay systems,” Proc. of the 39th IEEE Conf. Decision and Control, pp. 2805–2810, 2000.

    Google Scholar 

  34. G. B. Koo, J. B. Park, and Y. H. Joo, “Exponential meansquare stabilisation for non-linear systems: sampled-data fuzzy control approach,” IET control Theory Appl., vol. 6, no. 18, pp. 2765–2774, 2012. [click]

    Article  MathSciNet  Google Scholar 

  35. A. Sala and C. Ari ˜ no, “Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: applications of Polya’s theorem,” Fuzzy Sets Syst., vol. 158, pp. 2671–2686, 2007. [click]

    Article  MathSciNet  MATH  Google Scholar 

  36. M. Narimani and H. K. Lam, “Relaxed LMI-based stability conditions for Takagi-Sugeno fuzzy control systems using regional-membership-function-shape-dependent analysis approach,” IEEE Trans. Fuzzy Syst., vol. 17, no. 5, pp. 1221–1228, 2009. [click]

    Article  Google Scholar 

  37. J. Dong and G. H. Yang, “Control synthesis of T-S fuzzy systems based on a new control scheme,” IEEE Trans. Fuzzy Syst., vol. 19, no. 2, pp. 323–338, 2011. [click]

    Article  Google Scholar 

  38. J. Qiu, H. Tian, Q. Lu, and H. Gao, “Nonsynchronized robust filtering design for continuous-time T-S fuzzy affine dynamic systems based on piecewise Lyapunov functions,” IEEE Trans. Cybern., vol. 43, no. 6, pp. 1755–1766, 2013. [click]

    Article  Google Scholar 

  39. J. Qiu, Y. Wei, and L. Wu, “A novel approach to reliable control of piecewise affine systems with actuator faults,” IEEE Trans. Circuits Syst. II, Exp. Briefs, to be published, DOI: 10.1109/TCSII.2016.2629663.

  40. J. Qiu, H. Gao, and S. X. Ding, “Recent advances on fuzzymodel-based nonlinear networked control systems: a survey,” IEEE Trans. Ind. Electron., vol. 63, no. 2, pp. 1207–1217, 2016. [click]

    Article  Google Scholar 

  41. E. Kim and H. Lee, “New approaches to relaxed quadratic stability conditions of fuzzy control systems,” IEEE Trans. Fuzzy Syst., vol. 8, no. 5, pp. 523–534, 2000. [click]

    Article  Google Scholar 

  42. S. G. Cao, N. W. Rees, and G. Feng, “Stability anaylsis and design for a class of continuous-time fuzzy control systems,” Int. J. Control, vol. 64, no. 6, pp. 1069–1087, 1996. [click]

    Article  MATH  Google Scholar 

  43. L. Xiaodong and Z. Qingling, “New approaches to H ∞ controller designs based on fuzzy observers for T-S fuzzy systems via LMI,” Automatica, vol. 39, no. 9, pp. 1571–1582, 2003. [click]

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Division of Electrical, Electronic and Control Engineering, Kongju National University, Gongju, 314-701, Korea

    Geun Bum Koo

  2. Department of Electrical and Electronic Engineering, Yonsei University, Seoul, 120-749, Korea

    Jin Bae Park

  3. Department of Control and Robotics Engineering, Kunsan National University, Kunsan, Chonbuk, 573-701, Korea

    Young Hoon Joo

Authors
  1. Geun Bum Koo
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  2. Jin Bae Park
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  3. Young Hoon Joo
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Corresponding author

Correspondence to Jin Bae Park.

Additional information

Recommended by Associate Editor Sun Jin Yoo under the direction of Editor Duk-Sun Shim. This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIP; Ministry of Science, ICT & Future Planning) (No. NRF-2017R1C1B1005422).

Geun Bum Koo received the B.S. and Ph.D. degrees in Electrical and Electronic Engineering from Yonsei University, Seoul, Korea, in 2007 and 2015, respectively. He is currently a professor in the Division of Electrical, Electronic and Control Engineering, Korea. His current research interests include large-scale systems, decentralized control, sampled-data control, digital redesign, nonlinear control, and fuzzy systems.

Jin Bae Park received the B.S. degree in electrical engineering from Yonsei University, Seoul, Korea, and the M.S. and Ph.D. degrees in electrical engineering from Kansas State University, Manhattan, KS, USA, in 1977, 1985, and 1990, respectively. Since 1992, he has been with the Department of Electrical and Electronic Engineering, Yonsei University, where he is currently a Professor. His major research interests include robust control and filtering, nonlinear control, intelligent mobile robot, drone, fuzzy logic control, neural networks, adaptive dynamic programming, chaos theory, and genetic algorithms. Dr. Park served as the Editor-in-Chief for the International Journal of Control, Automation, and Systems (2006-2010), the President for the Institute of Control, Robot, and Systems Engineers (2013), and the Senior Vice-President for Yonsei University (2015-2016).

Young Hoon Joo received the B.S., M.S., and Ph.D. degrees in electrical engineering fromYonsei University, Seoul, Korea, in 1982, 1984, and 1995, respectively. He worked with Samsung Electronics Company, Seoul, Korea, from 1986 to 1995, as a Project Manager. He was with the University of Houston, Houston, TX, USA, from 1998 to 1999, as a Visiting Professor with the Department of Electrical and Computer Engineering. He is currently a Professor with the Department of Control and Robotics Engineering, Kunsan National University, Kunsan, Korea. His major research interests include the field of intelligent robot, robot vision, intelligent control, human robot interaction, wind-farm control, and intelligent surveillance systems. Dr. Joo served as the President for the Korea Institute of Intelligent Systems (2008-2009), Vice-President for the Korean Institute of Electrical Engineers (2013-2014), and the Editor-in-Chief for the International Journal of Control, Automation, and Systems (2014-2017).

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Koo, G.B., Park, J.B. & Joo, Y.H. Intelligent Digital Redesign for Sampled-data Fuzzy Control Systems Based on State-matching Error Cost Function Approach. Int. J. Control Autom. Syst. 16, 350–359 (2018). https://doi.org/10.1007/s12555-017-0166-3

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