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Fuzzy-approximation-based decentralized adaptive control for pure-feedback large-scale nonlinear systems with time-delay

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Abstract

This paper focuses on the problem of decentralized adaptive fuzzy control for a class of pure-feedback large-scale nonlinear systems with time-delay. By combining fuzzy logical systems’ universal approximation capability with adaptive backstepping technique, an adaptive fuzzy control scheme is proposed. It is proved that the developed controller guarantees that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded in mean square. Simulation results are provided to demonstrate the effectiveness of the proposed control scheme.

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References

  1. Krstić M, Kanellakopoulos I, Kokotovic PV (1995) Nonlinear and adaptive control design. Wiley, New York

    Google Scholar 

  2. Shi P, Xia Y, Liu G, Rees D (2006) On designing of sliding-mode control for stochastic jump systems. IEEE Trans Autom Control 51(1):97–103

    Article  MathSciNet  Google Scholar 

  3. Wu LG, Su XJ, Shi P (2012) Sliding mode control with bounded L2 gain performance of markovian jump singular time-delay systems. Automatica 48(8):1929–1933

    Article  MathSciNet  MATH  Google Scholar 

  4. Yin S, Li X, Gao H, Kaynak O (2014) Data-based techniques focused on modern industry: an overview. IEEE Trans Ind Electron. doi:10.1109/TIE.2014.2308133

  5. Jiang ZP, Hill DJ (1999) A robust adaptive backstepping scheme for nonlinear systems with unmodeled dynamics. IEEE Trans Autom Control 44(9):1705–1711

    Article  MathSciNet  MATH  Google Scholar 

  6. Chen M, Ge SS, How BVE, Choo YS (2013) Robust adaptive position mooring control for marine vessels. IEEE Trans Control Syst Technol 21(2):395–409

    Article  Google Scholar 

  7. Chen M, Ge SS, Ren BB (2011) Adaptive tracking control of uncertain MIMO nonlinear systems with input constraints. Automatica 47(3):452–455

    Article  MathSciNet  MATH  Google Scholar 

  8. Hu QL, Ma GF, Xie LH (2008) Robust and adaptive variable structure output feedback control of uncertain systems with input nonlinearity. Automatica 44(4):552–559

    Article  MathSciNet  MATH  Google Scholar 

  9. Zhao XD, Zhang LX, Shi P, Karimi HR (2013) Novel stability criteria for T–S fuzzy systems. IEEE Trans Fuzzy Syst 21(6):1–11

    Article  Google Scholar 

  10. Tong SC, Chen B, Wang YF (2005) Fuzzy adaptive output feedback control for MIMO nonlinear systems. Fuzzy Sets Syst 156(2):285–299

    Article  MathSciNet  MATH  Google Scholar 

  11. Wang T, Tong SC, Li YM (2013) Adaptive neural network output feedback control of stochastic nonlinear systems with dynamical uncertainties. Neural Comput Appl 23(5):1481–1494

    Article  MathSciNet  Google Scholar 

  12. Chen M, Ge SS (2013) Direct adaptive neural control for a class of uncertain nonaffine nonlinear systems based on disturbance observer. IEEE Trans Cybern 43(4):1213–1225

    Article  Google Scholar 

  13. Tong SC, Li Y, Li YM, Liu YJ (2011) Observer-based adaptive fuzzy backstepping control for a class of stochastic nonlinear strict-feedback systems. IEEE Trans Syst Man Cybern Part B Cybern 41(6):1693–1704

    Article  MathSciNet  Google Scholar 

  14. Tong SC, Wang T, Li YM, Chen B (2012) A combined backstepping and stochastic small-gain approach to robust adaptive fuzzy output feedback control. IEEE Trans Fuzzy Syst 21(2):314–321

    Article  Google Scholar 

  15. Liu YJ, Chen CLP, Wen GX, Tong SC (2011) Adaptive neural output feedback tracking control for a class of uncertain discrete-time nonlinear systems. IEEE Trans Neural Netw 22(7):1162–1167

    Article  Google Scholar 

  16. Li TS, Tong SC, Feng G (2010) A novel robust adaptive fuzzy tracking control for a class of nonlinear multi-input/multi-output systems. IEEE Trans Fuzzy Syst 18(1):150–160

    Article  Google Scholar 

  17. Bououden S, Chadli M, Allouani F, Filali S (2013) A new approach for fuzzy predictive adaptive controller design using particle swarm optimization algorithm. Int J Innov Comput Inf Control 9(9):3741–3758

    Google Scholar 

  18. Sefriti S, Boumhidi J, Benyakhlef M, Boumhidi I (2013) Adaptive decentralized sliding mode neural network control of a class of nonlinear interconnected systems. Int J Innov Comput Inf Control 9(7):2941–2947

  19. Su XJ, Shi P, Wu LG, Song YD (2013) A novel control design on discrete-time Takagi–Sugeno fuzzy systems with time-varying delays. IEEE Trans Fuzzy Syst 20(6):655–671

    Article  Google Scholar 

  20. Su XJ, Shi P, Wu LG, Nguang SK (2013) Induced \(\ell _2\) filtering of fuzzy stochastic systems with time-varying delays. IEEE Trans Cybern 43(4):1251–1264

    Article  Google Scholar 

  21. Ge SS, Wang C (2002) Adaptive NN control of uncertain nonlinear pure-feedback systems. Automatica 38(4):671–682

    Article  MathSciNet  MATH  Google Scholar 

  22. Wang D, Huang J (2002) Adaptive neural network control for a class of uncertain nonlinear systems in pure-feedback form. Automatica 38(8):1365–1372

    Article  MathSciNet  MATH  Google Scholar 

  23. Wang C, Hill DJ, Ge SS, Chen GR (2006) An ISS-modular approach for adaptive neural control of pure-feedback systems. Automatica 42(5):723–731

    Article  MathSciNet  MATH  Google Scholar 

  24. Zhang TP, Ge SS (2008) Adaptive dynamic surface control of nonlinear systems with unknown dead zone in pure feedback form. Automatica 44(7):1895–1903

    Article  MathSciNet  MATH  Google Scholar 

  25. Li YM, Tong SC (2013) Adaptive fuzzy output-feedback control of pure-feedback uncertain nonlinear systems with unknown dead-zone. IEEE Trans Fuzzy Syst. doi:10.1109/TFUZZ.2013.2280146

  26. Li YM, Tong SC, Li TS (2013) Direct adaptive fuzzy backstepping control of uncertain nonlinear systems in the presence of input saturation. Neural Comput Appl 23(5):1207–1216

    Article  MathSciNet  Google Scholar 

  27. Wang HQ, Chen B, Liu XP, Liu KF, Lin C (2013) Robust adaptive fuzzy tracking control for pure-feedback stochastic nonlinear systems with input constraints. IEEE Trans Cybern 43(6):2093–2104

    Article  Google Scholar 

  28. Wang HQ, Chen B, Lin C (2013) Adaptive neural tracking control for a class of perturbed pure-feedback nonlinear systems. Nonlinear Dyn 72(1–2):207–220

    Article  MathSciNet  MATH  Google Scholar 

  29. Tong SC, Li YM, Shi P (2012) Observer-based adaptive fuzzy backstepping output feedback control of uncertain MIMO pure-feedback nonlinear systems. IEEE Trans Fuzzy Syst 20(4):771–785

    Article  Google Scholar 

  30. Wang M, Ge SS, Hong KS (2010) Approximation-based adaptive tracking control of pure-feedback nonlinear systems with multiple unknown time-varying delays. IEEE Trans Neural Netw 21(11):804–1816

    Google Scholar 

  31. Niculescu S-L (2001) Delay effects on stability: a robust control approach. Springer, London

    Google Scholar 

  32. Gao H, Meng X, Chen T (2008) Stabilization of networked control systems with a new delay characterization. IEEE Trans Autom Control 53(9):2142–2148

    Article  MathSciNet  Google Scholar 

  33. Chen Y, Zheng WX (2011) Stability and L2 performance analysis of stochastic delayed neural networks. IEEE Trans Neural Netw 22(10):1662–1668

    Article  Google Scholar 

  34. Qiu J, Feng G, Yang J (2009) A new design of delay-dependent robust H-infinity filtering for discrete-time T–S fuzzy systems with time-varying delay. IEEE Trans Fuzzy Syst 17(5):1044–1058

    Article  Google Scholar 

  35. Hua CC, Liu PX, Guan XP (2009) Backstepping control for nonlinear systems with time delays and applications to chemical reactor systems. IEEE Trans Ind Electron 56(9):3723–3732

    Article  Google Scholar 

  36. Jiao X, Shen T (2005) Adaptive feedback control of nonlinear timedelay systems: the LaSalle–Razumikhin-based approach. IEEE Trans Autom Control 50(11):1909–1913

    Article  MathSciNet  Google Scholar 

  37. Ge SS, Hong F, Lee TH (2003) Adaptive neural network control of nonlinear systems with unknown time delays. IEEE Trans Autom Control 48(11):2004–2010

    Article  MathSciNet  Google Scholar 

  38. Chen B, Liu XP, Liu KF, Lin C (2010) Fuzzy approximation-based adaptive control of strict-feedback nonlinear systems with time delays. IEEE Trans Fuzzy Syst 18(5):883–892

    Article  MathSciNet  Google Scholar 

  39. Chen B, Liu XP, Liu KF, Lin C (2009) Novel adaptive neural control design for nonlinear MIMO time-delay systems. Automatica 45(6):1554–1560

    Article  MathSciNet  MATH  Google Scholar 

  40. Wang HQ, Chen B, Lin C (2013) Adaptive neural tracking control for a class of stochastic nonlinear systems with unknown dead-zone. Int J Innov Comput Inf Control 9(8):3257–3269

    Google Scholar 

  41. Datta A (1993) Performance improvement in decentralized adaptive control: a model reference scheme. IEEE Trans Autom Control 38(11):1717–1722

    Article  MATH  Google Scholar 

  42. Wen CY (1994) Decentralized adaptive regulation. IEEE Trans Autom Control 39(10):2163–2166

    Article  MATH  Google Scholar 

  43. Liu X, Huang G (2001) Global decentralized robust stabilization for interconnected uncertain nonlinear systems with multiple inputs. Automatica 37(9):1435–1442

    Article  MATH  Google Scholar 

  44. Zhang HG, Cai L (2002) Decentralized nonlinear adaptive control of an HVAC system. IEEE Trans Syst Man Cybern Part C Appl Rev 32(4):493–498

    Article  Google Scholar 

  45. Zhou J, Wen CY (2008) Decentralized backstepping adaptive output tracking of interconnected nonlinear systems. IEEE Trans Autom Control 53(10):2378–2384

    Article  MathSciNet  Google Scholar 

  46. Tong SC, Huo BY, Li YM (2014) Observer-based adaptive decentralized fuzzy fault-tolerant control of nonlinear large-scale systems with actuator failures. IEEE Trans Fuzzy Syst 22(1):1–15

    Article  Google Scholar 

  47. Tong SC, Liu CL, Li YM (2010) Fuzzy adaptive decentralized control for large-scale nonlinear systems with dynamical uncertainties. IEEE Trans Fuzzy Syst 18(5):845–861

    Article  Google Scholar 

  48. Tong SC, Li YM, Zhang HG (2011) Adaptive neural network decentralized backstepping output-feedback control for nonlinear large-scale systems with time delays. IEEE Trans Neural Netw 22(7):1073–1086

    Article  Google Scholar 

  49. Tong SC, Li YM (2013) Adaptive fuzzy decentralized output feedback control for nonlinear large-scale systems with unknown dead zone inputs. IEEE Trans Fuzzy Syst 21(5):913–925

    Article  Google Scholar 

  50. Chen WS, Li JM (2008) Decentralized output-feedback neural control for systems with unknown interconnections. IEEE Trans Syst Man Cybern Part B Cybern 38(1):258–266

    Article  Google Scholar 

  51. Karimi B, Menhaj MB (2010) Non-affine nonlinear adaptive control of decentralized large-scale systems using neural networks. Inf Sci 180(17):3335–3347

    Article  MathSciNet  MATH  Google Scholar 

  52. Huang YS, Wu M (2011) Robust decentralized direct adaptive output feedback fuzzy control for a class of large-sale nonaffine nonlinear systems. Inf Sci 181(11):2392–2404

    Article  MATH  Google Scholar 

  53. Ge SS, Wang J (2002) Robust adaptive neural control for a class of perturbed strict feedback nonlinear systems. IEEE Trans Neural Netw 13(6):1409–1419

    Article  Google Scholar 

  54. Apostol TM (1963) Mathematical analysis. Addison-Wesley, Reading, MA

    Google Scholar 

  55. Li J, Chen WS, Li JM (2011) Adaptive NN output-feedback decentralized stabilization for a class of large-scale stochastic nonlinear strict-feedback systems. Int J Robust Nonlinear Control 21(4):452–472

    Article  MATH  Google Scholar 

  56. Wang LX, Mendel JM (1992) Fuzzy basis functions, universal approximation, and orthogonal least squares learning. IEEE Trans Neural Netw 3(5):807–814

    Article  Google Scholar 

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Acknowledgments

This work is partially supported by the Natural Science Foundation of China (61304002 and 61304003), the Program for New Century Excellent Talents in University (NECT-13-0696), the Program for Liaoning Innovative Research Team in University under Grant (LT2013023), and by the Education Department of Liaoning Province under the general project research Grant (L2013424).

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Authors and Affiliations

  1. School of Mathematics and Physics, Bohai University, Jinzhou, 121000, Liaoning, People’s Republic of China

    Huanqing Wang

  2. College of Engineering, Bohai University, Jinzhou, 121000, Liaoning, People’s Republic of China

    Xuebo Yang & Zhandong Yu

  3. Faculty of Engineering, Lakehead University, Thunder Bay, ON, P7B 5E1, Canada

    Kefu Liu & Xiaoping Liu

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  1. Huanqing Wang
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  2. Xuebo Yang
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  3. Zhandong Yu
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  4. Kefu Liu
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  5. Xiaoping Liu
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Correspondence to Huanqing Wang.

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Wang, H., Yang, X., Yu, Z. et al. Fuzzy-approximation-based decentralized adaptive control for pure-feedback large-scale nonlinear systems with time-delay. Neural Comput & Applic 26, 151–160 (2015). https://doi.org/10.1007/s00521-014-1711-0

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  • DOI: https://doi.org/10.1007/s00521-014-1711-0

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