Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Adaptive Fuzzy Output-Feedback Tracking Control for a Class of Switched Stochastic Nonlinear Time-Delay Systems

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

In this paper, a design scheme for an adaptive fuzzy tracking controller is proposed for a class of switched stochastic nonlinear time-delay systems via dynamic output-feedback. First, a reduced-order observer is introduced to estimate the unmeasurable states of the switched system. During the adaptive controller design procedure, an appropriate stochastic Lyapunov–Krasovskii functional deals with the time-delay terms, and fuzzy logic systems are employed to approximate the unknown nonlinearities. Based on the designed controller, the semi-globally uniform ultimate boundedness of all the closed-loop signals is guaranteed and the tracking error converges to a small neighborhood of the origin. Finally, a simulation example is given to illustrate the validity of the proposed approach.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. G.X. Chen, Z.R. Xiang, M.S. Mahmoud, Stability and \(H_{\infty }\) performance analysis of switched stochastic neutral systems. Circuits Syst. Signal Process. 32(1), 387–400 (2013)

    Article  MathSciNet  Google Scholar 

  2. W.S. Chen, L.C. Jiao, J. Li, R.H. Li, Adaptive NN backstepping output-feedback control for stochastic nonlinear strict-feedback systems with time-varying delays. IEEE Trans. Syst. Man Cybern. B Cybern. 40(3), 939–950 (2010)

    Article  Google Scholar 

  3. H. Deng, M. Krstić, Stochastic nonlinear stabilization. Part I: a backstepping design. Syst. Control Lett. 32(3), 143–150 (1997)

    Article  MATH  Google Scholar 

  4. H. Deng, M. Krstić, Output-feedback stochastic nonlinear stabilization. IEEE Trans. Autom. Control 44(2), 328–333 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  5. H. Deng, M. Krstić, R.J. Williams, Stabilization of stochastic nonlinear systems driven by noise of unknown covariance. IEEE Trans. Autom. Control 46(8), 1237–1253 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  6. J. Fu, R.C. Ma, T.Y. Chai, Global finite-time stabilization of a class of switched nonlinear systems with the powers of positive odd rational numbers. Automatica 54, 360–373 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  7. H.J. Gao, X.Y. Meng, T.W. Chen, J. Lam, Stabilization of networked control systems via dynamic output-feedback controllers. SIAM J. Control Optim. 48(5), 3643–3658 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  8. M.Z. Hou, F.Y. Fu, G.R. Duan, Global stabilization of switched stochastic nonlinear systems in strict-feedback form under arbitrary switchings. Automatica 49, 2571–2575 (2013)

    Article  MathSciNet  Google Scholar 

  9. C.C. Hua, X.P. Guan, P. Shi, Robust backstepping control for a class of time delayed systems. IEEE Trans. Autom. Control 50(6), 894–899 (2005)

    Article  MathSciNet  Google Scholar 

  10. C.C. Hua, Q.G. Wang, X.P. Guan, Adaptive fuzzy output-feedback controller design for nonlinear time-delay systems with unknown control direction. IEEE Trans. Syst. Man Cybern. B Cybern. 39(2), 363–374 (2009)

    Article  Google Scholar 

  11. S.N. Huang, K.K. Tan, T.H. Lee, An improvement on stable adaptive control for a class of nonlinear systems. IEEE Trans. Autom. Control 49(8), 1398–1403 (2004)

    Article  MathSciNet  Google Scholar 

  12. M. Krstić, I. Kanellakopoulous, P.V. Kokotović, Nonlinear and Adaptive Control Design (Wiley Interscience, New York, 1995)

    Google Scholar 

  13. I. Kanellakopoulous, P.V. Kokotović, A.S. Morse, Systematic design of adaptive controller for feedback linearizable systems. IEEE Trans. Autom. Control 36(11), 1241–1253 (1991)

    Article  MATH  Google Scholar 

  14. H.Y. Li, H.J. Gao, P. Shi, X.D. Zhao, Fault-tolerant control of Markovian jump stochastic systems via the augmented sliding mode observer approach. Automatica 50(7), 1825–1834 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  15. H.Y. Li, X.J. Jing, H.R. Karimi, Output-feedback-based \(H_{\infty }\) control for vehicle suspension systems with control delay. IEEE Trans. Ind. Electron. 61(1), 436–446 (2014)

    Article  Google Scholar 

  16. H.Y. Li, Y.N. Pan, Q. Zhou, Filter design for interval type-2 fuzzy systems with D stability constraints under a unified frame. IEEE Trans. Fuzzy Syst. 23(3), 719–725 (2015)

    Article  Google Scholar 

  17. T.S. Li, S.C. Tong, G. Feng, 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 (2010)

    Article  Google Scholar 

  18. Y.M. Li, S.C. Tong, T.S. Li, Adaptive fuzzy backstepping control design for a class of pure-feedback switched nonlinear systems. Nonlinear Anal. Hybrid Syst. 16, 72–80 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  19. H.Y. Li, C.W. Wu, P. Shi, Y.B. Gao, Control of nonlinear networked systems with packet dropouts: interval type-2 fuzzy model-based approach. IEEE Trans. Cybern. (2014). doi:10.1109/TCYB.2014.2371814

  20. H.Y. Li, S. Yin, Y.N. Pan, H.K. Lam, Model reduction for interval type-2 Takagi-Sugeno fuzzy systems. Automatica (2015). doi:10.1016/j.automatica.2015.08.020

  21. J. Lian, C. Mu, P. Shi, Asynchronous \(H_{\infty }\) filtering for switched stochastic systems with time-varying delay. Inf. Sci. 224(1), 200–212 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  22. J. Lian, P. Shi, Z. Feng, Passivity and passification for a class of uncertain switched stochastic time-delay systems. IEEE Trans. Cybern. 43(1), 3–13 (2013)

    Article  Google Scholar 

  23. W. Lin, C.J. Qian, Adaptive control of nonlinearly parameterized systems: a nonsmooth feedback framework. IEEE Trans. Autom. Control 47(5), 757–774 (2002)

    Article  MathSciNet  Google Scholar 

  24. Y.J. Liu, S.C. Tong, W. Wang, Adaptive fuzzy output tracking control for a class of uncertain nonlinear systems. IEEE Trans. Fuzzy Syst. 160(19), 2727–2754 (2009)

    MathSciNet  MATH  Google Scholar 

  25. H. Liu, Y. Shen, X.D. Zhao, Asynchronous finite-time control for switched linear systems via mode-dependent dynamic state-feedback. Nonlinear Anal. Hybrid Syst. 8, 109–120 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  26. H. Liu, X.D. Zhao, Finite-time \(H_{\infty }\) control of switched systems with mode-dependent average dwell time. J. Frankl. Inst. 351(3), 1301–1315 (2014)

    Article  Google Scholar 

  27. L. J. Long, J. Zhao, Adaptive output-feedback neural control of switched uncertain nonlinear systems with average dwell time. IEEE Trans. Neural Netw. Learn. Syst. 26(7), 1350–1362 (2015)

  28. J. Napoles, A.J. Watson, J.J. Padilla, J. Leon, L.G. Franquelo, P.W. Wheeler, M.A. Aguirre, Selective harmonic mitigation technique for cascaded H-bridge converters with nonequal DC link voltages. IEEE Trans. Ind. Electron. 60(5), 1963–1971 (2013)

    Article  Google Scholar 

  29. B. Niu, J. Zhao, Barrier Lyapunov functions for the output tracking control of constrained nonlinear switched systems. Syst. Control Lett. 62(10), 963–971 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  30. Z.G. Pan, T. Basar, Backstepping controller design for nonlinear stochastic systems under a risk-sensitive cost criterion. SIAM J. Control Optim. 37(3), 957–995 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  31. J.B. Qiu, G. Feng, H.J. Gao, Approaches to robust \(H_{\infty }\) static output feedback control of discrete-time piecewise-affine systems with norm-bounded uncertainties. Int. J. Robust. Nonlinear Control 21(7), 790–814 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  32. E. Romero-Cadaval, G. Spagnuolo, L.G. Franquelo, C.A. Ramos-Paja, T. Suntio, W.M. Xiao, Grid-connected photovoltaic generation plants: Components and operation. IEEE Ind. Electron. M. 7(3), 6–20 (2013)

    Article  Google Scholar 

  33. K. Tanaka, M. Sano, A robust stabilization problem of fuzzy control systems and its applications to backing up control of a truck-trailer. IEEE Trans. Fuzzy Syst. 2(2), 119–134 (1994)

    Article  Google Scholar 

  34. S.C. Tong, C.L. Liu, Y.M. Li, Fuzzy-adaptive decentralized output-feedback control for large-scale nonlinear systems with dynamical uncertainties. IEEE Trans. Fuzzy Syst. 18(5), 845–861 (2010)

    Article  Google Scholar 

  35. L. Vu, K.A. Morgansen, Stability of time-delay feedback switched linear systems. IEEE Trans. Autom. Control 55(10), 2385–2390 (2010)

    Article  MathSciNet  Google Scholar 

  36. M. Wang, B. Chen, X.P. Liu, P. Shi, Adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear time-delay systems. Fuzzy Sets Syst. 159(8), 949–967 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  37. T. Wang, H.J. Gao, J.B. Qiu, A combined adaptive neural network and nonlinear model predictive control for multirate networked industrial process control. IEEE Trans. Neural Netw. Learn. Syst. (2015). doi:10.1109/TNNLS.2015.2411671

  38. H.Q. Wang, X.P. Liu, K.F. Liu, H.R. Karimi, Approximation-based adaptive fuzzy tracking control for a class of non-strict-feedback stochastic nonlinear time-delay systems. IEEE Trans. Fuzzy Syst. (2014). doi:10.1109/TFUZZ.2014.2375917

  39. L.X. Wang, J.M. Mendel, Fuzzy basis functions, universal approximation, and orthogonal least-squares learning. IEEE Trans. Neural Netw. 3(5), 807–814 (1992)

    Article  Google Scholar 

  40. Y.E. Wang, X.M. Sun, J. Zhao, Stabilization of a class of switched stochastic systems with time delays under asynchronous switching. Circuits Syst. Signal Process. 32(1), 347–360 (2013)

    Article  MathSciNet  Google Scholar 

  41. Z.J. Wu, X.J. Xie, S.Y. Zhang, Adaptive backstepping controller design using stochastic small-gain theorem. Automatica 43(4), 608–620 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  42. L.G. Wu, W.X. Zheng, H.J. Gao, Dissipativity-based sliding mode control of switched stochastic systems. IEEE Trans. Autom. Control 58(3), 785–793 (2013)

    Article  MathSciNet  Google Scholar 

  43. X.J. Xie, N. Duan, X. Yu, State-feedback control of high-order stochastic nonlinear systems with SiISS inverse dynamics. IEEE Trans. Autom. Control 56(8), 1921–1926 (2011)

    Article  MathSciNet  Google Scholar 

  44. S. Yin, S.X. Ding, A.H. Haghani, H.Y. Hao, Data-driven monitoring for stochastic systems and its application on batch process. Int. J. Syst. Sci. 44(7), 1366–1376 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  45. S. Yin, X.W. Li, H.J. Gao, O. Kaynak, Data-based techniques focused on modern industry: An overview. IEEE Trans. Ind. Electron. 62(1), 657–667 (2015)

    Article  Google Scholar 

  46. H.Y. Yue, J.M. Li, Output-feedback adaptive fuzzy control for a class of non-linear time-varying delay systems with unknown control directions. IET Control Theory Appl. 6(9), 1266–1280 (2012)

    Article  MathSciNet  Google Scholar 

  47. H.Y. Yue, J.M. Li, Adaptive fuzzy tracking control for a class of perturbed nonlinear time-varying delays systems with unknown control direction. Int. J. Uncertain. Fuzzy 21(4), 497–531 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  48. J.F. Zhang, Z.Z. Han, F.B. Zhu, X.D. Zhao, Absolute exponential stability and stabilization of switched nonlinear systems. Syst. Control Lett. 66, 51–57 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  49. J.F. Zhang, J. Huang, X.D. Zhao, Further results on stability and stabilisation of switched positive systems. IET Control Theory Appl. (2014). doi:10.1049/iet-cta.2014.1344

  50. Y. Zhao, H.J. Gao, Fuzzy-model-based control of an overhead crane with input delay and actuator saturation. IEEE Trans. Fuzzy Syst. 20(1), 181–186 (2012)

    Article  Google Scholar 

  51. X.D. Zhao, L.X. Zhang, P. Shi, M. Liu, Stability and stabilization of switched linear systems with mode-dependent average dwell time. IEEE Trans. Autom. Control 57(7), 1809–1815 (2012)

    Article  MathSciNet  Google Scholar 

  52. X.D. Zhao, L.X. Zhang, P. Shi, M. Liu, Stability of switched positive linear systems with average dwell time switching. Automatica 48(6), 1132–1137 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  53. Q. Zhou, P. Shi, H.H. Liu, S.Y. Xu, Neural-network-based decentralized adaptive output-feedback control for large-scale stochastic nonlinear systems. IEEE Trans. Syst. Man Cybern. B Cybern. 42(6), 1608–1619 (2012)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Mathematics and Physics and Automation Research Institute, Bohai University, Jinzhou, 121013, Liaoning, People’s Republic of China

    Yanli Liu & Ben Niu

  2. Jiangsu Province Laboratory of Electrical and Automation Engineering for Coal Mining, China University of Mining and Technology, Xuzhou, 221116, Jiangsu, People’s Republic of China

    Fei Chu

  3. AVIC Shenyang Engine Design and Research Institute, Shenyang, 110015, Liaoning, People’s Republic of China

    Yanyan Liu

Authors
  1. Yanli Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ben Niu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fei Chu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yanyan Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ben Niu.

Additional information

This work is supported by the National Nature Science Foundation of China (Nos. 61304054, 61403041, 61403354), the Program for Liaoning Provincial Excellent Talents in University, China (No. LJQ2014122).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, Y., Niu, B., Chu, F. et al. Adaptive Fuzzy Output-Feedback Tracking Control for a Class of Switched Stochastic Nonlinear Time-Delay Systems. Circuits Syst Signal Process 35, 2762–2788 (2016). https://doi.org/10.1007/s00034-015-0174-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-015-0174-6

Keywords

Search

Navigation