Skip to main content
SpringerLink
Log in

Observer-based adaptive neural network control for a class of MIMO uncertain nonlinear time-delay non-integer-order systems with asymmetric actuator saturation

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

This paper focuses on the adaptive neural output feedback control of a class of uncertain multi-input–multi-output nonlinear time-delay non-integer-order systems with unmeasured states, unknown control direction, and unknown asymmetric saturation actuator. Thus, the mean value theorem and a Gaussian error function-based continuous differentiable model are used in the paper to describe the unknown asymmetric saturation actuator and to get an affine model in which the control input appears in a linear fashion, respectively. The design of the controller follows a number of steps. Firstly, based on the semigroup property of fractional-order derivative, the system is transformed into a normalized fractional-order system by means of a state transformation in order to facilitate the control design. Then, a simple linear state observer is constructed to estimate the unmeasured states of the transformed system. A neural network is incorporated to approximate the unknown nonlinear functions while a Nussbaum function is used to deal with the unknown control direction. In addition, the strictly positive real condition, the Razumikhin Lemma, the frequency-distributed model, and the Lyapunov method are utilized to derive the parameter adaptive laws and to perform the stability proof. The main advantages of this work are that: (1) it can handle systems with constant, time-varying, and distributed time-varying delays, (2) the considered class of systems is relatively large, (3) the number of adjustable parameters is reduced, (4) the tracking errors converge asymptotically to zero and all signals of the closed-loop system are bounded. Finally, some simulation examples are provided to demonstrate the validity and effectiveness of the proposed scheme.

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

Access this article

Log in via an institution

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
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Yu Z, Li S, Yu Z (2016) Adaptive neural control for a class of pure-feedback nonlinear time-delay systems with asymmetric saturation actuators. Neurocomputing 173(3):1461–1470

    Article  MathSciNet  Google Scholar 

  2. Shi W (2015) Observer-based direct adaptive fuzzy control for single-input single-output non-linear systems with unknown gain sign. IET Control Theory Appl 9(17):2506–2513

    Article  MathSciNet  Google Scholar 

  3. Cui G, Wang Z, Zhuang G, Li Z, Chu Y (2015) Adaptive decentralized NN control of large-scale stochastic nonlinear time-delay systems with unknown dead-zone inputs. Neurocomputing 158:194–203

    Article  Google Scholar 

  4. Yu Z, Du H (2011) Adaptive neural control for uncertain stochastic nonlinear strict-feedback systems with time-varying delays: a Razumikhin functional method. Neurocomputing 74(12–14):2072–2082

    Article  Google Scholar 

  5. Chen B, Liu X, Liu K, Shi P, Lin C (2010) Direct adaptive fuzzy control for nonlinear systems with time-varying delays. Inf Sci 180(5):776–792

    Article  MathSciNet  MATH  Google Scholar 

  6. Boulkroune A, Bouzeriba A, Bouden T (2016) Fuzzy generalized projective synchronization of incommensurate fractional-order chaotic systems. Neurocomputing 173(3):606–614

    Article  MATH  Google Scholar 

  7. Miao B, Li T (2015) A novel neural network-based adaptive control for a class of uncertain nonlinear systems in strict-feedback form. Nonlinear Dyn 79(2):1005–1013

    Article  MathSciNet  Google Scholar 

  8. Shi W (2015) Observer-based fuzzy adaptive control for multi-input multi-output nonlinear systems with a nonsymmetric control gain matrix and unknown control direction. Fuzzy Sets Syst 236:1–26

    Article  MathSciNet  MATH  Google Scholar 

  9. Bouzeriba A, Boulkroune A, Bouden T (2015) Fuzzy adaptive synchronization of a class of fractional-order chaotic systems. Int Conf Control Eng Inf Technol 3:1–6

    MATH  Google Scholar 

  10. Boulkroune A, M’Saad M, Farza M (2012) Adaptive fuzzy tracking control for a class of MIMO nonaffine uncertain systems. Neurocomputing 93:48–55

    Article  Google Scholar 

  11. Boulkroune A, M’Saad M (2012) On the design of observer-based fuzzy adaptive controller for nonlinear systems with unknown control gain sign. Neurocomputing 201:71–85

    MathSciNet  MATH  Google Scholar 

  12. Boulkroune A, Tadjine M, M’Saad M, Farza M (2014) Design of a unified adaptive fuzzy observer for uncertain nonlinear systems. Inf Sci 265:139–153

    Article  MathSciNet  MATH  Google Scholar 

  13. Boulkroune A, M’Saad M (2011) A practical projective synchronization approach for uncertain chaotic systems with dead-zone input. Commun Nonlinear Sci Numer Simul 16(11):4487–4500

    Article  MathSciNet  MATH  Google Scholar 

  14. Boulkroune A, Bounar N, M’Saad M, Farza M (2014) Indirect adaptive fuzzy control scheme based on observer for nonlinear systems: a novel SPR-filter approach. Neurocomputing 135:378–387

    Article  Google Scholar 

  15. Sui S, Tong S, Li Y (2015) Observer-based fuzzy adaptive prescribed performance tracking control for nonlinear stochastic systems with input saturation. Neurocomputing 158:100–108

    Article  Google Scholar 

  16. Iqbal M, Rehan M, Hong K-S, Khaliq A, S-u Rehman (2015) Sector-condition based results for adaptive control and synchronization of chaotic systems under input saturation. Chaos, Solitons Fractals 77:158–169

    Article  MathSciNet  MATH  Google Scholar 

  17. Wang H, Liu X, Liu K (2015) Adaptive neural data-based compensation control of non-linear systems with dynamic uncertainties and input saturation. IET Control Theory Appl 9(7):1058–1065

    Article  MathSciNet  Google Scholar 

  18. Wang Q, Zhou B, Duan G-R (2015) Robust gain scheduled control of spacecraft rendezvous system subject to input saturation. Aerosp Sci Technol 42:442–450

    Article  Google Scholar 

  19. Liu Y-H, Huang L, Xiao D, Guo Y (2015) Global adaptive control for uncertain nonaffine nonlinear hysteretic systems. ISA Trans 58:255–261

    Article  Google Scholar 

  20. Du H, Chen X (2009) NN-based output feedback adaptive variable structure control for a class of non-affine nonlinear systems: a nonseparation principle design. Neurocomputing 72(7–9):2009–2016

    Article  Google Scholar 

  21. Mizumoto I, Fujii S, Ikejiri M (2015) Control of a magnetic levitation system via output feedback based two DOF control with an adaptive predictive feedforward input. IEEE conference on control applications, pp 71–76

  22. Shahnazi R (2016) Observer-based adaptive interval type-2 fuzzy control of uncertain MIMO nonlinear systems with unknown asymmetric saturation actuators. Neurocomputing 171:1053–1065

    Article  Google Scholar 

  23. Wei Y, Chen Y, Liang S, Wang Y (2015) A novel algorithm on adaptive backstepping control of fractional order systems. Neurocomputing 165:395–402

    Article  Google Scholar 

  24. Lan Y-H, Zhou Y (2013) Non-fragile observer-based robust control for a class of fractional-order nonlinear systems. Syst Control Lett 62(12):1143–1150

    Article  MathSciNet  MATH  Google Scholar 

  25. N’Doye I, Meriem T, Kirati L (2015) Fractional-order adaptive fault estimation for a class of nonlinear fractional-order systems. American control conference, pp 3804–3809

  26. Li C, Wang J (2014) Robust adaptive observer for fractional order nonlinear systems: an LMI approach. The 26th Chinese Control and decision conference, pp 392–397

  27. Vargas-De-León C (2015) Volterra-type Lyapunov functions for fractional-order epidemic systems. Commun Nonlinear Sci Numer Simul 24(1–3):75–85

    Article  MathSciNet  Google Scholar 

  28. Chen B, Chen J (2015) Razumikhin-type stability theorems for functional fractional-order differential systems and applications. Appl Math Comput 254:63–69

    MathSciNet  Google Scholar 

  29. Stamova I, Stamov G (2014) Stability analysis of impulsive functional systems of fractional order. Commun Nonlinear Sci Numer Simul 19(3):702–709

    Article  MathSciNet  Google Scholar 

  30. Stamova I, Stamov G (2013) Lipschitz stability criteria for functional differential systems of fractional order. J Math Phys 54(4). Article 043502

  31. Lan Y-H, Huang H-X, Zhou Y (2012) Observer-based robust control of a (1 ≤ a < 2) fractional-order uncertain systems: a linear matrix inequality approach. IET Control Theory Appl 6(2):229–234

    Article  MathSciNet  Google Scholar 

  32. Zhang Z, Xu S, Zhang B (2015) Exact tracking control of nonlinear systems with time delays and dead-zone input. Automatica 52:272–276

    Article  MathSciNet  MATH  Google Scholar 

  33. Ladaci S, Charef A, Loiseau J (2009) Robust fractional adaptive control based on the strictly positive realness condition. Int J Appl Math Comput Sci 19(1):69–76

    Article  MathSciNet  MATH  Google Scholar 

  34. Farges C, Moze M, Sabatier J (2010) Pseudo-state feedback stabilization of commensurate fractional order systems. Automatica 46(10):1730–1734

    Article  MathSciNet  MATH  Google Scholar 

  35. Lazarević M-P, Spasić A-M (2009) Finite-time stability analysis of fractional order time-delay systems: Gronwall’s approach. Math Comput Model 94(3–4):475–481

    Article  MathSciNet  MATH  Google Scholar 

  36. Lim Y-H, Oh K-K, Ahn H-S (2013) Stability and stabilization of fractional-order linear systems subject to input saturation. IEEE Trans Autom Control 58(4):1062–1067

    Article  MathSciNet  MATH  Google Scholar 

  37. Domek S, Dworak P (2016) Theoretical developments and applications of non-integer order systems. 7th conference on non-integer order calculus and its applications, Szczecin, Poland, lecture notes in electrical engineering 357

  38. Luo J, Liu H (2014) Adaptive fractional fuzzy sliding mode control for multivariable nonlinear systems. Discrete Dynamics in Nature and Society 2014. Article ID 541918, 10 p

  39. Liu K, Jiang W (2013) Uniform stability of fractional neutral systems: a Lyapunov–Krasovskii functional approach. Adv Differ Equ. doi:10.1186/1687-1847-2013-379

  40. Li Y, Tong S, Li T (2015) Observer-based adaptive fuzzy tracking control of MIMO stochastic nonlinear systems with unknown control directions and unknown dead zones. IEEE Trans Fuzzy Syst 23(4):1228–1241

    Article  Google Scholar 

  41. Li Y, Tong S, Li T (2015) Hybrid fuzzy adaptive output feedback control design for MIMO time-varying delays uncertain nonlinear systems. IEEE Trans Fuzzy Syst. doi:10.1109/TFUZZ.2015.2486811

    Google Scholar 

  42. Li Y, Tong S, Li T (2015) Composite adaptive fuzzy output feedback control design for uncertain nonlinear strict-feedback systems with input saturation. IEEE Trans Cybern 45(10):2299–2308

    Article  Google Scholar 

  43. McGarry K, Sarfraz M, MacIntyre J (2007) Integrating gene expression data from microarrays using the self-organising map and the gene ontology. In: Proceedings of second IAPR international workshop on pattern recognition in bioinformatics (PRIB 2007), Singapore, pp 206–217

  44. Rădac MB, Precup RE, Petriu EM, Preitl S (2014) Iterative data-driven tuning of controllers for nonlinear systems with constraints. IEEE Trans Ind Electron 61(11):6360–6368

    Article  Google Scholar 

  45. Yacoub RR, Bambang RT, Harsoyo A, Sarwono J (2014) DSP implementation of combined FIR-functional link neural network for active noise control. Int J Artif Intell 12(1):36–47

    Google Scholar 

  46. Yan P, Liu D, Wang D, Ma H (2016) Data-driven controller design for general MIMO nonlinear systems via virtual reference feedback tuning and neural networks. Neurocomputing 171:815–825

    Article  Google Scholar 

  47. Liu YJ, Gao Y, Tong S, Li Y (2016) Fuzzy approximation-based adaptive backstepping optimal control for a class of nonlinear discrete-time systems with dead-zone. IEEE Trans Fuzzy Syst 24(1):16–28

    Article  Google Scholar 

  48. Gao Y, Liu YJ (2016) Adaptive fuzzy optimal control using direct heuristic dynamic programming for chaotic discrete-time system. J Vib Control 22(2):595–603

    Article  MathSciNet  Google Scholar 

  49. Liu YJ, Tong S (2014) Adaptive fuzzy control for a class of nonlinear discrete-time systems with backlash. IEEE Trans Fuzzy Syst 22(5):1359–1365

    Article  Google Scholar 

  50. Liu YJ, Tong S (2015) Adaptive fuzzy identification and control for a class of nonlinear pure-feedback MIMO systems with unknown dead zones. IEEE Trans Fuzzy Syst 23(5):1387–1398

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  52. Bouzeriba A, Boulkroune A, Bouden T (2015) Projective synchronization of two different fractional-order chaotic systems via adaptive fuzzy control. Neural Comput Appl. doi:10.1007/s00521-015-1938-4

    MATH  Google Scholar 

  53. Chen L, Liu C, Wu R, He Y, Chai Y (2016) Finite-time stability criteria for a class of fractional-order neural networks with delay. Neural Comput Appl 27(3):549–556

    Article  Google Scholar 

  54. Wang F, Yang Y, Xu X, Li L (2015) Global asymptotic stability of impulsive fractional-order BAM neural networks with time delay. Neural Comput Appl. doi:10.1007/s00521-015-2063-0

    Google Scholar 

  55. Ibeas A, de la Sen M (2007) Robust sliding control of robotic manipulators based on a heuristic modification of the sliding gain. J Intell Rob Syst 48(4):485–511

    Article  Google Scholar 

  56. Tabatabaei SM, Arefi MM (2016) Adaptive neural control for a class of uncertain non-affine nonlinear switched system. Nonlinear Dyn 83(3):1773–1781

    Article  MathSciNet  MATH  Google Scholar 

  57. Arefi MM, Jahed-Motlagh MR, Karimi HR (2014) Adaptive neural stabilizing controller for a class of mismatched uncertain nonlinear systems by state and output feedback. IEEE Trans Cybern 45(8):1587–1596

    Article  Google Scholar 

  58. Arefi MM, Ramezani Z, Jahed-Motlagh MR (2014) Observer-based adaptive robust control of nonlinear nonaffine systems with unknown gain sign. Nonlinear Dyn 78(3):2185–2194

    Article  MathSciNet  MATH  Google Scholar 

  59. Petras I (2011) Fractional-order nonlinear systems: modeling, analysis and simulation. Nonlinear Physical Science, Springer, Berlin

    Book  MATH  Google Scholar 

  60. Boulkroune A, M’Saad M, Chekireb H (2010) Design of a fuzzy adaptive controller for MIMO nonlinear time-delay systems with unknown actuator nonlinearities and unknown control direction. Inf Sci 180(24):5041–5059

    Article  MathSciNet  MATH  Google Scholar 

  61. Ioannou PA, Sun J (1996) Robust adaptive control. Prentice Hall Neurocomputing, Englewood Cliffs

    MATH  Google Scholar 

  62. Boulkroune A, M’saad M, Farza M (2016) Adaptive fuzzy system-based variable-structure controller for multivariable nonaffine nonlinear uncertain systems subject to actuator nonlinearities. Neural Comput Appl. doi:10.1007/s00521-016-2241-8

    MATH  Google Scholar 

  63. Yue H, Li J (2012) 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

    Article  MathSciNet  Google Scholar 

  64. Liu S, Jiang W, Li X, Zhou XF (2016) Lyapunov stability analysis of fractional nonlinear systems. Appl Math Lett 51:13–19

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

The authors would like to express their sincere appreciation and gratitude to the Editor, Associate Editor, and anonymous reviewers for their constructive comments and suggestions, and for their time and efforts spent in helping us to improve the quality and presentation of the manuscript. The third author is grateful to the Spanish Ministry of Economy and Competitiveness (MINECO) for its financial support through Grant No. DPI2013-47825-C3-1-R.

Author information

Authors and Affiliations

  1. Laboratoire de Recherche LARA-Automatique, École Nationale d’Ingénieurs de Tunis, Université de Tunis El Manar, La Belvédère, B.P 37, 1002, Tunis, Tunisia

    Farouk Zouari

  2. LAJ, University of Jijel, Ouled-Aissa, BP. 98, 18000, Jijel, Algeria

    Abdesselem Boulkroune

  3. Department of Telecommunications and Systems Engineering, Universitat Autònoma de Barcelona, Bellaterra, 08193, Barcelona, Spain

    Asier Ibeas

  4. Department of Power and Control Engineering, School of Electrical and Computer Engineering, Shiraz University, Shiraz, 71348-51154, Iran

    Mohammad Mehdi Arefi

Authors
  1. Farouk Zouari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Abdesselem Boulkroune
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Asier Ibeas
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mohammad Mehdi Arefi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Abdesselem Boulkroune.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zouari, F., Boulkroune, A., Ibeas, A. et al. Observer-based adaptive neural network control for a class of MIMO uncertain nonlinear time-delay non-integer-order systems with asymmetric actuator saturation. Neural Comput & Applic 28 (Suppl 1), 993–1010 (2017). https://doi.org/10.1007/s00521-016-2369-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-016-2369-6

Keywords

Search

Navigation