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Hybrid Neural Network Control for Uncertain Nonlinear Discrete-Time Systems with Bounded Disturbance

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Abstract

This paper has proposed an adaptive control scheme based on a hybrid neural network (HNN) to address the problem of uncertain nonlinear systems with discrete-time having bounded disturbances. This proposed control scheme is composed of a neural network (NN) and differential evolution (DE) technique which is used to initialize the weights of the NN and the controller is designed in such a manner so that the stability can be ensured and the desired trajectory can be achieved. The designed HNN is employed to approximate unknown functions present in the system. By using the concept of system transformation, the adaptive law and controller are designed and the whole system is proved to be stable in the sense of semi-globally uniformly ultimately boundedness (SGUUB) with the assistance of Lyapunov theory. Finally, the validity and effectiveness of the results are proved through two simulation examples.

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References

  1. Lian, Y., Zhou, Y., Zhang, J., Ma, S., & Wu, S. (2022). An Intelligent Nonlinear Control Method for the Multistage Electromechanical Servo System. Applied Sciences, 12(10), 5053.

    Article  Google Scholar 

  2. Cruz-Zavala, E., Nuño, E., & Moreno, J. A. (2021). Robust trajectory-tracking in finite-time for robot manipulators using nonlinear proportional-derivative control plus feed-forward compensation. International Journal of Robust and Nonlinear Control, 31(9), 3878–3907.

    Article  MathSciNet  Google Scholar 

  3. Gong, P., Yan, Z., Zhang, W., & Tang, J. (2021). Lyapunov-based model predictive control trajectory tracking for an autonomous underwater vehicle with external disturbances. Ocean Engineering, 232, 109010.

    Article  Google Scholar 

  4. Bacciotti, A., & Rosier, L. (2005). Liapunov functions and stability in control theory. Heidelberg: Springer Science & Business Media.

    Book  MATH  Google Scholar 

  5. Esfandiari, F., & Khalil, H. K. (1992). Output feedback stabilization of fully linearizable systems. International Journal of control, 56(5), 1007–1037.

    Article  MathSciNet  MATH  Google Scholar 

  6. Jiang, B., Karimi, H. R., Kao, Y., & Gao, C. (2019). Reduced-order adaptive sliding mode control for nonlinear switching semi-Markovian jump delayed systems. Information Sciences, 477, 334–348.

    Article  MathSciNet  MATH  Google Scholar 

  7. Lei, H., & Lin, W. (2005). Universal output feedback control of nonlinear systems with unknown growth rate. IFAC Proceedings Volumes, 38(1), 1073–1078.

    Article  Google Scholar 

  8. Li, F., & Liu, Y. (2017). Global finite-time stabilization via time-varying output-feedback for uncertain nonlinear systems with unknown growth rate. International Journal of Robust and Nonlinear Control, 27(17), 4050–4070.

    MathSciNet  MATH  Google Scholar 

  9. Li, Y., Li, K., & Tong, S. (2018). Finite-time adaptive fuzzy output feedback dynamic surface control for MIMO nonstrict feedback systems. IEEE Transactions on Fuzzy Systems, 27(1), 96–110.

    Article  Google Scholar 

  10. Miao, P., Shen, Y., Li, Y., & Bao, L. (2016). Finite-time recurrent neural networks for solving nonlinear optimization problems and their application. Neurocomputing, 177, 120–129.

    Article  Google Scholar 

  11. Singh, U. P., & Jain, S. (2016). Modified chaotic bat algorithm based counter propagation neural network for uncertain nonlinear discrete time system. International Journal of Computational Intelligence and Applications, 15(03), 1650016.

    Article  Google Scholar 

  12. Chen, B., Liu, X., Liu, K., & Lin, C. (2009). Direct adaptive fuzzy control of nonlinear strict-feedback systems. Automatica, 45(6), 1530–1535.

    Article  MathSciNet  MATH  Google Scholar 

  13. Chen, B., Liu, X., Liu, K., & Lin, C. (2010). Fuzzy-approximation-based adaptive control of strict-feedback nonlinear systems with time delays. IEEE Transactions on Fuzzy Systems, 18(5), 883–892.

    Article  Google Scholar 

  14. Singh, U. P., Jain, S., Gupta, R. K., & Tiwari, A. (2019). AFMBC for a class of nonlinear discrete-time systems with dead zone. International Journal of Fuzzy Systems, 21(4), 1073–1084.

    Article  MathSciNet  Google Scholar 

  15. Tong, S., Min, X., & Li, Y. (2020). Observer-based adaptive fuzzy tracking control for strict-feedback nonlinear systems with unknown control gain functions. IEEE Transactions on Cybernetics, 50(9), 3903–3913.

    Article  Google Scholar 

  16. Das, M., & Mahanta, C. (2014). Optimal second order sliding mode control for linear uncertain systems. ISA transactions, 53(6), 1807–1815.

    Article  Google Scholar 

  17. Shaocheng, T., Changying, L., & Yongming, L. (2009). Fuzzy adaptive observer backstepping control for MIMO nonlinear systems. Fuzzy sets and systems, 160(19), 2755–2775.

    Article  MathSciNet  MATH  Google Scholar 

  18. Mobayen, S., & Majd, V. J. (2012). Robust tracking control method based on composite nonlinear feedback technique for linear systems with time-varying uncertain parameters and disturbances. Nonlinear Dynamics, 70(1), 171–180.

    Article  MathSciNet  MATH  Google Scholar 

  19. Ho, H. F., Wong, Y. K., & Rad, A. B. (2009). Adaptive fuzzy sliding mode control with chattering elimination for nonlinear SISO systems. Simulation Modelling Practice and Theory, 17(7), 1199–1210.

    Article  Google Scholar 

  20. Lee, H. (2010). Robust adaptive fuzzy control by backstepping for a class of MIMO nonlinear systems. IEEE Transactions on Fuzzy Systems, 19(2), 265–275.

    Article  Google Scholar 

  21. Chen, B., Liu, X., Liu, K., & Lin, C. (2009). Novel adaptive neural control design for nonlinear MIMO time-delay systems. Automatica, 45(6), 1554–1560.

    Article  MathSciNet  MATH  Google Scholar 

  22. Zhou, Q., Zhao, S., Li, H., Lu, R., & Wu, C. (2018). Adaptive neural network tracking control for robotic manipulators with dead zone. IEEE Transactions on Neural Networks and Learning Systems, 30(12), 3611–3620.

    Article  MathSciNet  Google Scholar 

  23. Chen, M., & Tao, G. (2015). Adaptive fault-tolerant control of uncertain nonlinear large-scale systems with unknown dead zone. IEEE Transactions on Cybernetics, 46(8), 1851–1862.

    Article  Google Scholar 

  24. Zhao, X., Shi, P., Zheng, X., & Zhang, L. (2015). Adaptive tracking control for switched stochastic nonlinear systems with unknown actuator dead-zone. Automatica, 60, 193–200.

    Article  MathSciNet  MATH  Google Scholar 

  25. Cao, L., Zhou, Q., Dong, G., & Li, H. (2019). Observer-based adaptive event-triggered control for nonstrict-feedback nonlinear systems with output constraint and actuator failures. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 51(3), 1380–1391.

    Article  Google Scholar 

  26. Xu, B., Sun, F., Pan, Y., & Chen, B. (2016). Disturbance observer based composite learning fuzzy control of nonlinear systems with unknown dead zone. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 47(8), 1854–1862.

    Article  Google Scholar 

  27. Chen, B., Liu, X., Liu, K., & Lin, C. (2013). Fuzzy approximation-based adaptive control of nonlinear delayed systems with unknown dead zone. IEEE Transactions on Fuzzy Systems, 22(2), 237–248.

    Article  Google Scholar 

  28. Liu, Y. J., Tong, S., Li, D. J., & Gao, Y. (2015). Fuzzy adaptive control with state observer for a class of nonlinear discrete-time systems with input constraint. IEEE Transactions on Fuzzy Systems, 24(5), 1147–1158.

    Article  Google Scholar 

  29. Liu, Y. J., Li, S., Tong, S., & Chen, C. P. (2018). Adaptive reinforcement learning control based on neural approximation for nonlinear discrete-time systems with unknown nonaffine dead-zone input. IEEE transactions on neural networks and learning systems, 30(1), 295–305.

    Article  Google Scholar 

  30. Liu, Y. J., Gao, Y., Tong, S., & Chen, C. P. (2015). A unified approach to adaptive neural control for nonlinear discrete-time systems with nonlinear dead-zone input. IEEE Transactions on Neural Networks and Learning Systems, 27(1), 139–150.

    Article  MathSciNet  Google Scholar 

  31. Singh, U. P., & Jain, S. (2018). Optimization of neural network for nonlinear discrete time system using modified quaternion firefly algorithm: case study of Indian currency exchange rate prediction. Soft Computing, 22(8), 2667–2681.

    Article  Google Scholar 

  32. Wei, Q., & Liu, D. (2015). Neural-network-based adaptive optimal tracking control scheme for discrete-time nonlinear systems with approximation errors. Neurocomputing, 149, 106–115.

    Article  Google Scholar 

  33. Na, J., Lv, Y., Wu, X., Guo, Y., & Chen, Q. (2014). Approximate optimal tracking control for continuous-time unknown nonlinear systems. In Proceedings of the 33rd chinese control conference (pp. 8990–8995). IEEE

  34. Zhou, Q., Shi, P., Lu, J., & Xu, S. (2011). Adaptive output-feedback fuzzy tracking control for a class of nonlinear systems. IEEE Transactions on Fuzzy Systems, 19(5), 972–982.

    Article  Google Scholar 

  35. Mehraeen, S., Jagannathan, S., & Crow, M. L. (2011). Decentralized dynamic surface control of large-scale interconnected systems in strict-feedback form using neural networks with asymptotic stabilization. IEEE Transactions on Neural Networks, 22(11), 1709–1722.

    Article  Google Scholar 

  36. Chen, W., & Li, J. (2008). Decentralized output-feedback neural control for systems with unknown interconnections. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 38(1), 258–266.

    Article  Google Scholar 

  37. Lee, T. H., & Narendra, K. (1986). Stable discrete adaptive control with unknown high-frequency gain. IEEE Transactions on Automatic Control, 31(5), 477–479.

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Mathematics, Shri Mata Vaishno Devi University, Katra, 182320, JK, India

    Rahul Kumar, Uday Pratap Singh, Arun Bali & Kuldip Raj

Authors
  1. Rahul Kumar
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  2. Uday Pratap Singh
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  3. Arun Bali
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  4. Kuldip Raj
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Contributions

RK: Conceptualization, Writing—original draft. UPS: Methodology, Validation, Writing. AB: Review, editing and software. KR: Supervision.

Corresponding author

Correspondence to Uday Pratap Singh.

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On behalf of the all authors, We declare that we have no conflict of interest in any terms like financial support from any organizations/institutions, data, code used in this paper etc.

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Kumar, R., Singh, U.P., Bali, A. et al. Hybrid Neural Network Control for Uncertain Nonlinear Discrete-Time Systems with Bounded Disturbance. Wireless Pers Commun 126, 3475–3494 (2022). https://doi.org/10.1007/s11277-022-09875-9

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