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An LMI approach to adaptive robust tracker design for uncertain nonlinear systems with time-delays and input nonlinearities

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Abstract

In this paper, the adaptive robust tracking and model following controller is designed for the uncertain nonlinear systems with disturbances, time-delays and input nonlinearities. A novel control law based on the linear matrix inequalities is proposed for the tracking control of the nonlinear systems with Lipschitz nonlinearities. The selection procedure of the nonlinear integral sliding surface and the existence of the proposed sliding mode are two significant subjects, which have been addressed. This controller guarantees that the tracking error decreases asymptotically to the origin in the presence of time-varying perturbations. By elimination of the reaching mode of the sliding surface, the robustness performance against perturbations is guaranteed right from the initial instant. Furthermore, the knowledge of the upper bounds of the uncertainties, disturbances and time-delays is not required to be determined. Simulation results are provided to illustrate the efficiency of the presented technique compared to the previous methods.

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References

  1. Mobayen, S.: Robust tracking controller for multivariable delayed systems with input saturation via composite nonlinear feedback. Nonlinear Dyn. 76(1), 827–838 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  2. Mobayen, S.: Design of a robust tracker and disturbance attenuator for uncertain systems with time delays. Complexity 21, 340–348 (2015)

    Article  MathSciNet  Google Scholar 

  3. Mobayen, S.: An LMI-based robust tracker for uncertain linear systems with multiple time-varying delays using optimal composite nonlinear feedback technique. Nonlinear Dyn. 80, 917–927 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  4. Mobayen, S., Baleanu, D., Tchier, F.: Second-order fast terminal sliding mode control design based on LMI for a class of non-linear uncertain systems and its application to chaotic systems. J. Vib. Control (2016). doi:10.1177/1077546315623887

  5. Mobayen, S., Tchier, F.: Design of an adaptive chattering avoidance global sliding mode tracker for uncertain non-linear time-varying systems. Trans. Inst. Meas. Control (2016). doi:10.1177/0142331216644046

  6. Mobayen, S.: Fast terminal sliding mode tracking of non-holonomic systems withf exponential decay rate. IET Control Theory Appl. 9(8), 1294–1301 (2015)

    Article  MathSciNet  Google Scholar 

  7. Ni, M.L., Li, G.: A direct approach to the design of robust tracking controllers for uncertain delay systems. Asian J. Control 8, 412–416 (2006)

    Article  MathSciNet  Google Scholar 

  8. Oucheriah, S.: Robust tracking and model following of uncertain dynamic delay systems by memoryless linear controllers. IEEE Trans. Autom. Control 44, 1473–1477 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  9. Wu, H.: Robust tracking and model following control with zero tracking error for uncertain dynamical systems. J. Optim. Theory Appl. 107, 169–182 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  10. Wu, H.: Adaptive robust tracking and model following of uncertain dynamical systems with multiple time delays. IEEE Trans. Autom. Control 49, 611–616 (2004)

    Article  MathSciNet  Google Scholar 

  11. Shigemaru, S., Wu, H.S.: Decentralized robust tracking and model following for uncertain large-scale interconnected systems. J. Optim. Theory Appl. 110, 35–52 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  12. Ni, M.L., Er, M.J., Leithead, W.E., Leith, D.J.: New approach to the design of robust tracking and model following controllers for uncertain delay systems. IEE Proc. Control Theory Appl. 148, 472–477 (2001)

    Article  Google Scholar 

  13. Wu, H.S.: Decentralized adaptive robust tracking and model following for large-scale systems including delayed state perturbations in the interconnections. J. Optim. Theory Appl. 137, 231–253 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  14. Wu, H.: Adaptive robust control of uncertain nonlinear systems with nonlinear delayed state perturbations. Automatica 45, 1979–1984 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  15. Wu, H.: Adaptive robust state observers for a class of uncertain nonlinear dynamical systems with delayed state perturbations. IEEE Trans. Autom. Control 54, 1407–1412 (2009)

  16. Pai, M.C.: Robust tracking and model following of uncertain dynamic systems via discrete-time integral sliding mode control. Int. J. Control Autom. Syst. 7(3), 381–387 (2009)

    Article  Google Scholar 

  17. Wu, H.: Decentralised adaptive controllers for robust tracking and model following of uncertain large scale systems. Int. J. Control 82(2), 268–278 (2009)

    Article  MATH  Google Scholar 

  18. Pai, M.C.: Design of adaptive sliding mode controller for robust tracking and model following. J. Frankl. Inst. 347, 1837–1849 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  19. Pai, M.C.: Observer-based adaptive sliding mode control for robust tracking and model following. Int. J. Control Autom. Syst. 11(2), 225–232 (2013)

    Article  Google Scholar 

  20. Pai, M.C.: Robust tracking and model following based on discrete-time neuro-sliding mode control for uncertain time-delay systems. Nonlinear Dyn. 73(1), 427–437 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  21. Pai, M.C.: Discrete-time sliding mode control for robust tracking and model following of systems with state and input delays. Nonlinear Dyn. 76(3), 1769–1779 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  22. Mobayen, S.: Finite-time robust-tracking and model-following controller for uncertain dynamical systems. J. Vib. Control 22(4), 1117–1127 (2016)

    Article  MathSciNet  Google Scholar 

  23. Pai, M.C.: Discrete-time output feedback quasi-sliding mode control for robust tracking and model following of uncertain systems. J. Frankl. Inst. 351(5), 2623–2639 (2014)

    Article  MathSciNet  Google Scholar 

  24. Pai, M.C.: Dynamic output feedback RBF neural network sliding mode control for robust tracking and model following. Nonlinear Dyn. 79(2), 1023–1033 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  25. Pai, M.C.: Robust tracking and model following for uncertain time-delay systems with input nonlinearity. Complexity 21, 66–73 (2015)

    Article  MathSciNet  Google Scholar 

  26. Mobayen, S.: Optimal LMI-based state feedback stabilizer for uncertain nonlinear systems with time-varying uncertainties and disturbances. Complexity (2015). doi:10.1002/cplx.21695

    MATH  Google Scholar 

  27. Mobayen, S.: Design of LMI-based sliding mode controller with an exponential policy for a class of underactuated systems. Complexity (2014). doi:10.1002/cplx.21636

    Google Scholar 

  28. Hilhorst, G., Pipeleers, G., Michiels, W., Swevers, J.: Sufficient LMI conditions for reduced-order multi-objective H\(_{2}\)/H\(_{8}\) control of LTI systems. Eur. J. Control 23, 17–25 (2015)

    Article  MathSciNet  Google Scholar 

  29. Haddad, W.M., Hui, Q., Chellaboina, V.: H\(_{2}\) optimal semistable control for linear dynamical systems: an LMI approach. J. Frankl. Inst. 348(10), 2898–2910 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  30. Yang, D., Cai, K.Y.: Reliable guaranteed cost sampling control for nonlinear time-delay systems. Math. Comput. Simul. 80, 2005–2018 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  31. Mobayen, S., Tchier, F.: A new LMI-based robust finite-time sliding mode control strategy for a class of uncertain nonlinear systems. Kybernetika 51(6), 1035–1048 (2015)

    MathSciNet  MATH  Google Scholar 

  32. Mobayen, S.: Design of LMI-based global sliding mode controller for uncertain nonlinear systems with application to Genesio’s chaotic system. Complexity 21(1), 94–98 (2015)

    Article  MathSciNet  Google Scholar 

  33. Mobayen, S.: An LMI-based robust controller design using global nonlinear sliding surfaces and application to chaotic systems. Nonlinear Dyn. 79, 1075–1084 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  34. Alfi, A., Bakhshi, A., Yousefi, M., Talebi, H.A.: Design and implementation of robust-fixed structure controller for telerobotic systems. J. Int. Robot. Syst. (2016). doi:10.1007/s10846-016-0335-2

    Google Scholar 

  35. Shokri-Ghaleh, H., Alfi, A.: Optimal synchronization of teleoperation systems via cuckoo optimization algorithm. Nonlinear Dyn. 78(4), 2359–2376 (2014)

    Article  MathSciNet  Google Scholar 

  36. Liu, Y.J., Tong, S.: Adaptive fuzzy control for a class of unknown nonlinear dynamical systems. Fuzzy Sets Syst. 263, 49–70 (2015)

    Article  MathSciNet  Google Scholar 

  37. Pai, M.C.: Chaos control of uncertain time-delay chaotic systems with input dead-zone nonlinearity. Complexity 21(3), 13–20 (2016)

    Article  MathSciNet  Google Scholar 

  38. Lin, D., Lan, W.: Output feedback composite nonlinear feedback control for singular systems with input saturation. J. Frankl. Inst. 352, 384–398 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  39. Pai, M.C.: Chaotic sliding mode controllers for uncertain time-delay chaotic systems with input nonlinearity. Appl. Math. Comput. 271, 757–767 (2015)

    MathSciNet  Google Scholar 

  40. Shyu, K.K., Liu, W.J., Hsu, K.C.: Design of large-scale time-delayed systems with dead-zone input via variable structure control. Automatica 41, 1239–1246 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  41. Rehan, M., Hong, K.S., Ge, S.S.: Stabilization and tracking control for a class of nonlinear systems. Nonlinear Anal. Real World Appl. 12, 1786–1796 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  42. Wu, H.: Adaptive robust control of uncertain dynamical systems with multiple time-varying delays. IET Control Theory Appl. 4, 1775–1784 (2010)

    Article  MathSciNet  Google Scholar 

  43. Majd, V.J., Mobayen, S.: An ISM-based CNF tracking controller design for uncertain MIMO linear systems with multiple time-delays and external disturbances. Nonlinear Dyn. 80, 591–613 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  44. Hopp, T.H., Schmitendorf, W.E.: Design of a linear controller for robust tracking and model following. Trans. ASME 112, 552–558 (1990)

    MATH  Google Scholar 

  45. Mobayen, S., Majd, V.J.: Robust tracking control method based on composite nonlinear feedback technique for linear systems with time-varying uncertain parameters and disturbances. Nonlinear Dyn. 70, 171–180 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  46. Mobayen, S.: Design of CNF-based nonlinear integral sliding surface for matched uncertain linear systems with multiple state-delays. Nonlinear Dyn. 77, 1047–1054 (2014)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgments

This research project was supported by a grant from the “Research Center of the Center for Female Scientific and Medical Colleges,” Deanship of Scientific Research, King Saud University.

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Authors and Affiliations

  1. Department of Electrical Engineering, University of Zanjan, P.O. Box 38791-45371, Zanjan, Iran

    Saleh Mobayen

  2. Department of Mathematics, King Saud University, P. O. Box 22452, Riyadh, 11495, Saudi Arabia

    Fairouz Tchier

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  1. Saleh Mobayen
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  2. Fairouz Tchier
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Correspondence to Saleh Mobayen.

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Mobayen, S., Tchier, F. An LMI approach to adaptive robust tracker design for uncertain nonlinear systems with time-delays and input nonlinearities. Nonlinear Dyn 85, 1965–1978 (2016). https://doi.org/10.1007/s11071-016-2809-y

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  • DOI: https://doi.org/10.1007/s11071-016-2809-y

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