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Non-fragile control of fuzzy affine dynamic systems via piecewise Lyapunov functions

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Abstract

This paper addresses the robust H static output feedback (SOF) controller design problem for a class of uncertain fuzzy affine systems that are robust against both the plant parameter perturbations and controller gain variations. More specifically, the purpose is to synthesize a non-fragile piecewise affine SOF controller guaranteeing the stability of the resulting closed-loop fuzzy affine dynamic system with certainH performance index. Based on piecewise quadratic Lyapunov functions and applying some convexification procedures, two different approaches are proposed to solve the robust and non-fragile piecewise affine SOF controller synthesis problem. It is shown that the piecewise affine controller gains can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, simulation examples are given to illustrate the effectiveness of the proposed methods.

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References

  1. Sala A, Guerra T M, Babuška R. Perspectives of fuzzy systems and control. Fuzzy Sets and Systems, 2005, 156(3): 432–444

    Article  MathSciNet  MATH  Google Scholar 

  2. Feng G. A survey on analysis and design of model-based fuzzy control systems. IEEE Transactions on Fuzzy Systems, 2006, 14(5): 676–697

    Article  Google Scholar 

  3. Takagi T, Sugeno M. Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions on Systems, Man and Cybernetics, 1985, SMC-15(1): 116–132

    Google Scholar 

  4. Tanaka K, Wang H O. Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. New York: Wiley, 2001

    Book  Google Scholar 

  5. Teixeira M C M, Żak S H. Stabilizing controller design for uncertain nonlinear systems using fuzzy models. IEEE Transactions on Fuzzy Systems, 1999, 7(2): 133–142

    Article  Google Scholar 

  6. Gao H, Chen T. Stabilization of nonlinear systems under variable sampling: a fuzzy control approach. IEEE Transactions on Fuzzy Systems, 2007, 15(5): 972–983

    Article  Google Scholar 

  7. Zhang C, Feng G, Gao H, Qiu J. H filtering for nonlinear discretetime systems subject to quantization and packet dropouts. IEEE Transactions on Fuzzy Systems, 2011, 19(2): 353–365

    Article  Google Scholar 

  8. Liu M, Cao X, Shi P. Fuzzy-model-based fault-tolerant design for nonlinear stochastic systems against simultaneous sensor and actuator faults. IEEE Transactions on Fuzzy Systems, 2013, 21(5): 789–799

    Article  Google Scholar 

  9. Qiu J, Gao H, Ding S X. Recent advances on fuzzy-model-based nonlinear networked control systems: a survey. IEEE Transactions on Industrial Electronics, 2016, 63(2): 1207–1217

    Article  Google Scholar 

  10. Li L, Ding S X, Qiu J, Yang Y. Real-time fault detection approach for nonlinear systems and its asynchronous T-S fuzzy observer-based implementation. IEEE Transactions on Cybernetics, doi: 10.1109/TCYB.2015.2513438

  11. Johansson M, Rantzer A, Årzén K E. Piecewise quadratic stability of fuzzy systems. IEEE Transaction on Fuzzy Systems, 1999, 7(6): 713–722

    Article  Google Scholar 

  12. Feng G, Chen C L, Sun D, Zhu Y. H controller synthesis of fuzzy dynamic systems based on piecewise Lyapunov functions and bilinear matrix inequalities. IEEE Transactions on Fuzzy Systems, 2005, 13(1): 94–103

    Article  Google Scholar 

  13. Qiu J, Feng G, Gao H. Observer-based piecewise affine output feedback controller synthesis of continuous-time T-S fuzzy affine dynamic systems using quantized measurements. IEEE Transactions on Fuzzy Systems, 2012, 20(6): 1046–1062

    Article  Google Scholar 

  14. Fu S, Wang M, Qiu J, He Y. T-S fuzzy affine model based nonsynchronized state estimation for nonlinear Itô stochastic systems. Neurocomputing, 2015, 167: 424–433

    Article  Google Scholar 

  15. Li L, Ding S X, Qiu J, Yang Y, Zhang Y. Weighted fuzzy observerbased fault detection approach for discrete-time nonlinear systems via piecewise-fuzzy Lyapunov functions. IEEE Transactions on Fuzzy Systems, doi: 10.1109/TFUZZ.2016.2514371

  16. Zhou K, Doyle J C, Glover K. Robust Optimal Control, Englewood Cliffs, NJ: Prentice Hall, 2001

    Google Scholar 

  17. Zhang C, Feng G, Qiu J, Shen Y. Control synthesis for a class of linear network-based systems with communication constraints. IEEE Transactions on Industrial Electronics, 2013, 60(8): 3339–3348

    Article  Google Scholar 

  18. Wei Y, Qiu J, Karimi H R, Wang M. H model reduction for continuous-time Markovian jump systems with incomplete statistics of mode information. International Journal of Systems Science, 2014, 45(7): 1496–1507

    Article  MathSciNet  MATH  Google Scholar 

  19. Qiu J, Wei Y, Karimi H R. New approach to delay-dependent H control for continuous-time Markovian jump systems with time-varying delay and deficient transition descriptions. Journal of The Franklin Institute, 2015, 352(1): 189–215

    Article  MathSciNet  MATH  Google Scholar 

  20. Wang T, Gao H, Qiu J. A combined adaptive neural network and nonlinear model predictive control for multirate networked industrial process control. IEEE Transactions on Neural Networks and Learning Systems, 2016, 27(2): 416–425

    Article  MathSciNet  Google Scholar 

  21. Keel L H, Bhattacharyya S P. Robust, fragile, or optimal? IEEE Transactions on Automatic Control, 1997, 42(8): 1098–1105

    Article  MathSciNet  MATH  Google Scholar 

  22. Du H, Lam J, Sze K Y. Design of non-fragile H controller for active vehicle suspensions. Journal of Vibration and Control, 2005, 11(2): 225–243

    MATH  Google Scholar 

  23. Zhang B, Zhou S, Li T. A new approach to robust and non-fragile H control for uncertain fuzzy systems. Information Sciences, 2007, 177(22): 5118–5133

    Article  MathSciNet  MATH  Google Scholar 

  24. Chen J D, Yang C D, Lien C H, Horng J H. New delay-dependent nonfragile H observer-based control for continuous time-delay systems. Information Sciences, 2008, 178(24): 4699–4706

    Article  MathSciNet  MATH  Google Scholar 

  25. Fan Y, Liu L, Feng G, Wang Y. Self-triggered consensus for multiagent systems with Zeno-free triggers. IEEE Transactions on Automatic Control, 2015, 60(10): 2779–2784

    Article  MathSciNet  MATH  Google Scholar 

  26. Mahmoud M S, Almutairi N B. Resilient decentralized stabilization of interconnected time-delay systems with polytopic uncertainties. International Journal of Robust and Nonlinear Control, 2011, 21(4): 355–372

    Article  MathSciNet  MATH  Google Scholar 

  27. Dadkhah N, Rodrigues L. Non-fragile state-feedback control of uncertain piecewise-affine slab systems with input constraints: a convex optimisation approach. IET Control Theory & Application, 2014, 8(8): 626–632

    Article  MathSciNet  Google Scholar 

  28. El Ghaoui L, Oustry F, AitRami M. A cone complementarity linearization algorithm for static output-feedback and related problems. IEEE Transactions on Automatic Control, 1997, 42(8): 1171–1176

    Article  MathSciNet  MATH  Google Scholar 

  29. Qiu J, Feng G, Gao H. Static-output-feedback control of continuoustime T-S fuzzy affine systems via piecewise Lyapunov functions. IEEE Transactions on Fuzzy Systems, 2013, 21(2): 245–261

    Article  Google Scholar 

  30. Kchaou M, El Hajjaji A, Toumi A. Non-fragile H output feedback control design for continuous-time fuzzy systems. ISA Transactions, 2015, 54: 3–14

    Article  Google Scholar 

  31. Syrmos V L, Abdallah C T, Dorato P, Grigoriadis K. Static output feedback-a survey. Automatica, 1997, 33(2): 125–137

    Article  MathSciNet  MATH  Google Scholar 

  32. Qiu J, Feng G, Gao H. Asynchronous output feedback control of networked nonlinear systems with multiple packet dropouts: T-S fuzzy affine model based approach. IEEE Transactions on Fuzzy Systems, 2011, 19(6): 1014–1030

    Article  Google Scholar 

  33. Wei Y, Qiu J, Karimi H R, Wang M. New results on H dynamic output feedback control for Markovian jump systems with time-varying delay and deficient mode information. Optimal Control Applications and Methods, 2014, 35(6): 656–675

    Article  MathSciNet  MATH  Google Scholar 

  34. Chen L, Huang X, Fu S. Observer-based sensor fault-tolerant control for semi-Markovian jump systems. Nonlinear Analysis: Hybrid Systems, 2016, 22: 161–177

    Article  MathSciNet  MATH  Google Scholar 

  35. Xie L. Output feedback H control of systems with parameter uncertainty. International Journal of Control, 1996, 63(4): 741–750

    Article  MathSciNet  MATH  Google Scholar 

  36. Boyd S, El Ghaoui L, Feron E, Balakrishnan V. Linear Matrix Inequality in Systems and Control Theory. Philadelphia: Society for Industrial and Applied Mathematics, 1994

    Book  MATH  Google Scholar 

  37. Qiu J, Ding S X, Gao H, Yin S. Fuzzy-model-based reliable static output feedback H control of nonlinear hyperbolic PDE systems. IEEE Transaction on Fuzzy Systems, 2016, 24(2): 388–400

    Article  Google Scholar 

  38. Wei Y, Qiu J, Lam H K, Wu L. Approaches to T-S fuzzy affine model based reliable output feedback control for nonlinear Itô stochastic systems. IEEE Transaction on Fuzzy Systems, doi: 10.1109/TFUZZ.2016.2566810

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (NSFC) (Grant No. 61522306). The authors are grateful to the Editor-in-Chief, the Associate Editor, and anonymous reviewers for their constructive comments based on which the presentation of this paper has been greatly improved.

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Correspondence to Jianbin Qiu.

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Shasha Fu received the BE degree in automation from Northeast Forestry University, China in 2012 and the ME degree in control science and engineering from Harbin Institute of Technology (HIT), China in 2014. She is currently pursuing the PhD degree in the Research Institute of Intelligent Control and Systems, HIT. Her research interests include fuzzy control, robust filtering and control, nonlinear systems, fault-tolerant control, and their engineering applications.

Jianbin Qiu received the BE and PhD degrees in mechanical and electrical engineering from the University of Science and Technology of China (USTC), China in 2004 and 2009, respectively. He also received the PhD degree in mechatronics engineering from the City University of Hong Kong, China in 2009. He has been with the School of Astronautics, Harbin Institute of Technology since 2009, where he is currently a full professor. Prof. Qiu is a senior member of IEEE and serves as the chairman of the IEEE Industrial Electronics Society Harbin Chapter, China. He is an associate editor of IEEE Transactions on Cybernetics. His current research interests include intelligent and hybrid control systems, signal processing, and robotics. He is the awardee of the NSFC Excellent Young Scholars Program in 2015.

Wenqiang JI received the Bachelor’s degree in automation from the Harbin Engineering University, China in 2012. He is currently pursuing his PhD in control science and engineering at School of Astronautics, Harbin Institute of Technology, China. His main research fields include fuzzy systems and control, robust control, and sliding-mode control.

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Fu, S., Qiu, J. & Ji, W. Non-fragile control of fuzzy affine dynamic systems via piecewise Lyapunov functions. Front. Comput. Sci. 11, 937–947 (2017). https://doi.org/10.1007/s11704-016-6138-6

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  • DOI: https://doi.org/10.1007/s11704-016-6138-6

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