Advertisement

Neural Computing and Applications

, Volume 31, Issue 4, pp 1201–1213 | Cite as

Fractional neural observer design for a class of nonlinear fractional chaotic systems

  • Amin Sharafian
  • Reza GhasemiEmail author
Original Article

Abstract

In this paper, a novel observer structure for nonlinear fractional-order systems is presented to estimate the states of fractional-order nonlinear chaotic system with unknown dynamical model. A new fractional error back-propagation learning algorithm is derived to adapt weights of the artificial neural network, by taking advantage of the Lyapunov stability strategy of fractional-order systems which is called Miattag–Leffler stability. The main contribution is the extension of neural observer for fractional dynamics in a way that satisfies Miattag–Leffler conditions. Observer design procedure guarantees the convergence of observer error to the neighborhood of zero. Furthermore, the robustness of the proposed estimator against uncertainties and external disturbances are the main benefits of the proposed method. Simulation results show the effectiveness and capabilities of the proposed observer.

Keywords

Fractional-order systems State estimation Artificial neural network Nonlinear observer Nonlinear systems 

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Human and animal rights

All the authors of the manuscript declared that there is no research involving human participants and/or animal and material that required informed consent.

References

  1. 1.
    Abdi B, Bahrami H, Ghiasi MI, Ghasemi R (2012) PM Machine Optimization in Variable Speed EMB Application. International Review of Electrical Engineering-IREE 7(3):4412–4418Google Scholar
  2. 2.
    Jiang B, Xu D, Shi P, Lim CC (2014) Adaptive neural observer-based backstepping fault tolerant control for near space vehicle under control effector damage. Control Theory Appl IET 8(9):658–666MathSciNetCrossRefGoogle Scholar
  3. 3.
    Sharafian A, Ghasemi R, (2016 In press) Stable State Dependent Riccati Equation neural observer for a class of nonlinear systems. International Journal of Modeling, Identification and controlGoogle Scholar
  4. 4.
    Ghasemi R (2013) Designing observer based variable structure controller for large scale nonlinear systems. IAES International Journal of Artificial Intelligence 2(3):125Google Scholar
  5. 5.
    Boukal Y, Darouach M, Zasadzinski M, Radhy NE (2014) H∞ observer design for linear fractional-order systems in time and frequency domains. In: Control conference (ECC), 2014 European. IEEE, pp 2975–2980Google Scholar
  6. 6.
    Lan YH, Zhou Y (2013) Non-fragile observer-based robust control for a class of fractional-order nonlinear systems. Syst Control Lett 62(12):1143–1150MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Ibrir S, Bettayeb M (2015) New sufficient conditions for observer-based control of fractional-order uncertain systems. Automatica 59:216–223MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Lu J, Xie W, Zhou H, Zhang A (2014) 1322. Vibration suppression using fractional-order disturbance observer based adaptive grey predictive controller. J Vibroeng 16(5):2205–2215Google Scholar
  9. 9.
    Achili B, Madani T, Daachi B, Djouani K (2016) Adaptive observer based on MLPNN and sliding mode for wearable robots: application to an active joint orthosis. Neurocomputing 197:69–77CrossRefGoogle Scholar
  10. 10.
    Wang H, Chen B, Lin C, Sun Y (2016) Observer-based adaptive neural control for a class of nonlinear pure-feedback systems. Neurocomputing 171:1517–1523CrossRefGoogle Scholar
  11. 11.
    Lakhal AN, Tlili AS, Braiek NB (2010) Neural network observer for nonlinear systems application to induction motors. Int J Control Autom 3(1):1–16Google Scholar
  12. 12.
    Khoygani MRR, Ghasemi R, Vali AR (2015) Intelligent nonlinear observer design for a class of nonlinear discrete-time flexible joint robot. Intel Serv Robot 8(1):45–56CrossRefGoogle Scholar
  13. 13.
    Shaik FA, Purwar S, Pratap B (2011) Real-time implementation of Chebyshev neural network observer for twin rotor control system. Expert Syst Appl 38(10):13043–13049CrossRefGoogle Scholar
  14. 14.
    Bouzeriba A, Boulkroune A, Bouden T (2015) Fuzzy adaptive synchronization of a class of fractional-order chaotic systems. In: Control, engineering and information technology (CEIT), 3rd international conference on 2015. IEEE, pp 1–6Google Scholar
  15. 15.
    Boulkroune A, Bouzeriba A, Bouden T, Azar AT (2016) Fuzzy adaptive synchronization of uncertain fractional-order chaotic systems. In: Azar A, Vaidyanathan S (eds) Advances in chaos theory and intelligent control. Studies in fuzziness and soft computing, vol 337. Springer, Cham. doi: 10.1007/978-3-319-30340-6_28 Google Scholar
  16. 16.
    Cruz-Victoria JC, Martínez-Guerra R, Pérez-Pinacho CA, Gómez-Cortés GC (2015) Synchronization of nonlinear fractional order systems by means of PI rα reduced order observer. Appl Math Comput 262:224–231MathSciNetzbMATHGoogle Scholar
  17. 17.
    Lan YH, Wang LL, Ding L, Zhou Y (2016) Full-order and reduced-order observer design for a class of fractional-order nonlinear systems. Asian J Control 18(4):1467–1477MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Djeghali N, Djennoune S, Bettayeb M, Ghanes M, Barbot JP (2016) Observation and sliding mode observer for nonlinear fractional-order system with unknown input. ISA Trans 63:1–10CrossRefGoogle Scholar
  19. 19.
    Tianyi Z, Xuemei R, Yao Z (2015) A fractional order sliding mode controller design for spacecraft attitude control system. In: Control conference (CCC), 2015 34th Chinese. IEEE, pp 3379–3382Google Scholar
  20. 20.
    Huang C, Cao J (2017) Active control strategy for synchronization and anti-synchronization of a fractional chaotic financial system. Statistical Mechanics and its Applications, Physica ACrossRefzbMATHGoogle Scholar
  21. 21.
    Huang C, Cao J, Xiao M, Alsaedi A, Hayat T (2017) Bifurcations in a delayed fractional complex-valued neural network. Appl Math Comput 292:210–227MathSciNetzbMATHGoogle Scholar
  22. 22.
    Huang C, Meng Y, Cao J, Alsaedi A, Alsaadi FE (2017) New bifurcation results for fractional BAM neural network with leakage delay. Chaos, Solitons Fractals 100:31–44MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Huang C, Cao J, Ma Z (2016) Delay-induced bifurcation in a tri-neuron fractional neural network. Int J Syst Sci 47(15):3668–3677MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Shaik FA, Purwar S (2009) A nonlinear state observer design for 2-DOF twin rotor system using neural networks. In: Presentation in international conference on advances in computing, control, and telecommunication technologies, Trivandrum, IndiaGoogle Scholar
  25. 25.
    Liu Y (2009) Robust adaptive observer design for nonlinear systems with unmodeled dynamics. Automatica 45:1891–1895MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Khoygani MRR, Ghasemi R (2016) Neural estimation using a stable discrete-time MLP observer for a class of discrete-time uncertain MIMO nonlinear systems. Nonlinear Dyn 84(4):1–17MathSciNetzbMATHGoogle Scholar
  27. 27.
    Chen B, Zhang H, Lin C (2016) Observer-based adaptive neural network control for nonlinear systems in nonstrict-feedback form. IEEE Trans Neural Netw Learn Syst 27(1):89–98MathSciNetCrossRefGoogle Scholar
  28. 28.
    Liu S, Li X, Jiang W, Zhou X (2012) Mittag–Leffler stability of nonlinear fractional neutral singular systems. Communications in Nonlinear Science and Numerical Simulation, 17(10), 3961-3966Google Scholar
  29. 29.
    Delavari H, Baleanu D, Sadati J (2012) Stability analysis of Caputo fractional-order nonlinear systems revisited. Nonlinear Dynamics 67(4):2433–2439MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Abdollahi F, Talebi HA, Patel RV (2006) A stable neural network-based observer with application to flexible-joint manipulators. IEEE Trans Neural Networks 17(1):118–129CrossRefGoogle Scholar
  31. 31.
    Liu S, Jiang W, Li X, Zhou XF (2016) Lyapunov stability analysis of fractional nonlinear systems. Applied Mathematics Letters 51:13–19MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Natural Computing Applications Forum 2017

Authors and Affiliations

  1. 1.Department of EngineeringUniversity of QomQomIran

Personalised recommendations