Skip to main content
SpringerLink
Log in

Adaptive control of unknown fuzzy disturbance-based uncertain nonlinear systems: application to hypersonic flight dynamics

  • Original Research Paper
  • Published:
The Journal of Analysis Aims and scope Submit manuscript

Abstract

Keeping into view the human-brain-like capabilities, a novel adaptive control scheme utilizing a defuzzification module has been designed in an effort to endow the control systems with human-like capabilities of learning and processing human-understandable information. It’s been noted that within real-time systems, uncertain and undefined external disruptions can manifest in various ways due to their ambiguous and unpredictable nature. Consequently, attempting to encapsulate these disturbances within precise closed-form mathematical expressions is often impractical. Therefore, opting to describe such ambiguous and incomplete information using linguistic variables, as opposed to rigid mathematical formulations, is a more suitable approach. In this regard, a novel class of uncertain nonlinear systems in non-strict feedback involving fuzzy variables is introduced in which the fuzzy variables are used to express unknown disturbances. As a result, such class is systems become more general and human-interactable but alongside the control of such class of systems becomes more complicated and difficult. Therefore, the goal of this work is to provide an efficient intelligent control technique for the proposed class of systems which can successfully handle these uncertainties and attributes of fuzziness. The proposed control scheme is therefore consists of (a) a defuzzification module to handle fuzzy variables and (b) radial basis function neural network (RBFNN) to approximate the unknown functions. The existing category of uncertain systems is managed by converting the system into an n-step ahead predictor and applying the suggested control approach. By leveraging Lyapunov theory, it can be demonstrated that the comprehensive closed-loop system achieves semi-global uniform ultimate boundedness (SGUUB), and it is established that the error tends to diminish towards zero. Additionally, the computational complexity of the overall control scheme is also analyzed. The control scheme is validated through numerical simulations for its effectiveness and real-time applicability. A simulation example based on hypersonic flight dynamics model developed by NASA-Langley Research Centre for longitudinal dynamics of a hypersonic vehicle is used to demonstrate the scheme’s reliability and real-time applicability.

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
Algorithm 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Data availability

Data sharing is not relevant to this research because no new data were created or reviewed in this research.

References

  1. Wang, G., and J. Qiao. 2021. An efficient self-organizing deep fuzzy neural network for nonlinear system modeling. IEEE Transactions on Fuzzy Systems 30 (7): 2170–2182. https://doi.org/10.1109/TFUZZ.2021.3077396.

    Article  Google Scholar 

  2. Madsen, E., O.S. Rosenlund, D. Brandt, and X. Zhang. 2020. Comprehensive modeling and identification of nonlinear joint dynamics for collaborative industrial robot manipulators. Control Engineering Practice 101: 104462. https://doi.org/10.1016/j.conengprac.2020.104462.

    Article  Google Scholar 

  3. Kumar, R., U. Pratap Singh, A. Bali, and K. Raj. 2022. Hybrid neural network control for uncertain nonlinear discrete-time systems with bounded disturbance. Wireless Personal Communications 126: 3475–3494. https://doi.org/10.1007/s11277-022-09875-9.

    Article  Google Scholar 

  4. Luongo, A., M.J. Leamy, S. Lenci, G. Piccardo, and C. Touze. 2021. Advances in stability, bifurcations and nonlinear vibrations in mechanical systems. Nonlinear Dynamics 103 (4): 2993–2995.

    Article  Google Scholar 

  5. Singh, A.P., D. Deb, H. Agrawal, and V.E. Balas. 2021. Modeling, Stability and Fractional Control of Single Flexible Link Robotic Manipulator. In Fractional Modeling and Controller Design of Robotic Manipulators, 83–98. Cham: Springer.

    Chapter  Google Scholar 

  6. Kumar, R., U.P. Singh, A. Bali, and S. Jain. 2022. Neuro-fuzzy elman wavelet control for nonlinear uncertain systems with fuzzy input and unknown fuzzy disturbances: Application to robotics. International Journal of Adaptive Control and Signal Processing 36 (12): 2988–3003.

    Article  MathSciNet  Google Scholar 

  7. Pang, H., R. Yao, P. Wang, and Z. Xu. 2021. Adaptive backstepping robust tracking control for stabilizing lateral dynamics of electric vehicles with uncertain parameters and external disturbances. Control Engineering Practice 110: 104781.

    Article  Google Scholar 

  8. Yang, Q., C.A. Sing-Long, and E. Reed. 2020. Rapid data-driven model reduction of nonlinear dynamical systems including chemical reaction networks using \(l^{1}\)-regularization. Chaos: An Interdisciplinary Journal of Nonlinear Science 30 (5): 053122.

    Article  MathSciNet  Google Scholar 

  9. Hao, R., H. Wang, S. Liu, M. Yang, and Z. Tian. 2021. Multi-objective command filtered adaptive control for nonlinear hydraulic active suspension systems. Nonlinear Dynamics 105 (2): 1559–1579.

    Article  Google Scholar 

  10. Li, C., Y. Mao, J. Zhou, N. Zhang, and X. An. 2017. Design of a fuzzy-pid controller for a nonlinear hydraulic turbine governing system by using a novel gravitational search algorithm based on cauchy mutation and mass weighting. Applied Soft Computing 52: 290–305.

    Article  Google Scholar 

  11. Bulín, R., Š Dyk, and M. Hajžman. 2021. Nonlinear dynamics of flexible slender structures moving in a limited space with application in nuclear reactors. Nonlinear Dynamics 104 (4): 3561–3579.

    Article  Google Scholar 

  12. Aboelezz, A., O. Mohamady, M. Hassanalian, and B. Elhadidi. 2021. Nonlinear flight dynamics and control of a fixed-wing micro air vehicle: Numerical, system identification and experimental investigations. Journal of Intelligent & Robotic Systems 101 (3): 1–18.

    Article  Google Scholar 

  13. Kumar, R., U.P. Singh, A. Bali, and S.S. Chouhan. 2023. It2-Neuro-Fuzzy Wavelet Network with Jordan Feedback Structure for the Control of Aerial Robotic Vehicles with External Disturbances. In Deep Learning and Other Soft Computing Techniques: Biomedical and Related Applications, 195–207. Cham: Springer.

    Chapter  Google Scholar 

  14. Sun, J., Z. Pu, J. Yi, and Z. Liu. 2019. Fixed-time control with uncertainty and measurement noise suppression for hypersonic vehicles via augmented sliding mode observers. IEEE Transactions on Industrial Informatics 16 (2): 1192–1203.

    Article  Google Scholar 

  15. Singh, P., et al. 2023. Ambiguous set theory: A new approach to deal with unconsciousness and ambiguousness of human perception. Journal of Neutrosophic and Fuzzy Systems 5 (1): 52–2.

    Article  Google Scholar 

  16. Singh, P. 2023. An investigation of ambiguous sets and their application to decision-making from partial order to lattice ambiguous sets. Decision Analytics Journal 8: 100286.

    Article  Google Scholar 

  17. Singh, P., and Y.-P. Huang. 2023. Membership functions, set-theoretic operations, distance measurement methods based on ambiguous set theory: A solution to a decision-making problem in selecting the appropriate colleges. International Journal of Fuzzy Systems 25: 1311–1326. https://doi.org/10.1007/s40815-023-01468-3.

    Article  Google Scholar 

  18. Lagrat, I., H. Ouakka, I. Boumhidi, et al. 2006. Fuzzy sliding mode pi controller for nonlinear systems. WSEAS Transactions on Signal Processing 2: 1137–1143.

    Google Scholar 

  19. Feng, Z., Z. Zhang, D. Pi. 2004. Open-closed-loop pd-type iterative learning controller for nonlinear systems and its convergence. In: Fifth World Congress on Intelligent Control and Automation (IEEE Cat. No. 04EX788), vol. 2, pp. 1241–1245, IEEE.

  20. Kim, J.-H., W.-C. Lee, and G.-T. Kang. 2003. Adaptive pid controller for nonlinear systems using fuzzy model. Journal of Korean Institute of Intelligent Systems 13 (1): 85–90.

    Article  Google Scholar 

  21. Sakhre, V., U. Singh, and S. Jain. 2017. Fcpn approach for uncertain nonlinear dynamical system with unknown disturbance. International Journal of Fuzzy Systems 19 (2): 452.

    Article  MathSciNet  Google Scholar 

  22. Singh, U.P., and S. Jain. 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 

  23. Nekoukar, V., and N.M. Dehkordi. 2021. Robust path tracking of a quadrotor using adaptive fuzzy terminal sliding mode control. Control Engineering Practice 110: 104763.

    Article  Google Scholar 

  24. Lin, Y.-C., V.E. Balas, J.-F. Yang, and Y.-H. Chang. 2020. Adaptive takagi-sugeno fuzzy model predictive control for permanent magnet synchronous generator-based hydrokinetic turbine systems. Energies 13 (20): 5296.

    Article  Google Scholar 

  25. Tan, S., J. Hao, J. Vandewalle. 1993. Nonlinear systems identification using rbf neural networks. In: Proceedings of 1993 International Conference on Neural Networks (IJCNN-93-Nagoya, Japan), vol. 2, pp. 1833–1836, IEEE.

  26. Kumar, R., S. Srivastava, and J. Gupta. 2017. Modeling and adaptive control of nonlinear dynamical systems using radial basis function network. Soft Computing 21 (15): 4447–4463.

    Article  Google Scholar 

  27. Song, R., W. Xiao, Q. Wei, and C. Sun. 2014. Neural-network-based approach to finite-time optimal control for a class of unknown nonlinear systems. Soft Computing 18 (8): 1645–1653.

    Article  Google Scholar 

  28. Wang, W., D. Wang, Z. Peng, and T. Li. 2015. Prescribed performance consensus of uncertain nonlinear strict-feedback systems with unknown control directions. IEEE Transactions on Systems, Man, and Cybernetics: Systems 46 (9): 1279–1286.

    Article  Google Scholar 

  29. Ma, H., H. Li, R. Lu, and T. Huang. 2020. Adaptive event-triggered control for a class of nonlinear systems with periodic disturbances. Science China Information Sciences 63 (5): 1–15.

    Article  MathSciNet  Google Scholar 

  30. Kumar, R., U. Pratap Singh, A. Bali, and K. Raj. 2022. Hybrid neural network controller for uncertain nonlinear discrete-time systems with non-symmetric dead zone and unknown disturbances. International Journal of Control 96 (8): 2003–2011. https://doi.org/10.1080/00207179.2022.2080117.

    Article  MathSciNet  Google Scholar 

  31. Kumar, R., U.P. Singh, A. Bali, and K. Raj. 2022. Hybrid neural network control for uncertain nonlinear discrete-time systems with bounded disturbance. Wireless Personal Communications 126 (4): 3475–3494.

    Article  Google Scholar 

  32. Bali, A., U. Pratap Singh, R. Kumar, and K. Raj. 2022. Hybrid neural network control for nonlinear continuous time systems with time delays and dead zone input. International Journal of Adaptive Control and Signal Processing 36 (6): 1439–1459. https://doi.org/10.1002/acs.3403.

    Article  MathSciNet  Google Scholar 

  33. Singh, U.P., and S. Jain. 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 

  34. Gil, P., T. Oliveira, and L. Palma. 2018. Adaptive neuro-fuzzy control for discrete-time nonaffine nonlinear systems. IEEE Transactions on Fuzzy Systems 27 (8): 1602–1615.

    Article  Google Scholar 

  35. Chairez, I. 2012. Differential neuro-fuzzy controller for uncertain nonlinear systems. IEEE Transactions on Fuzzy Systems 21 (2): 369–384.

    Article  Google Scholar 

  36. Song, S., J.H. Park, B. Zhang, X. Song, and Z. Zhang. 2020. Adaptive command filtered neuro-fuzzy control design for fractional-order nonlinear systems with unknown control directions and input quantization. IEEE Transactions on Systems, Man, and Cybernetics: Systems 51 (11): 7238–7249.

    Article  Google Scholar 

  37. Cervantes, J., W. Yu, S. Salazar, and I. Chairez. 2016. Takagi-sugeno dynamic neuro-fuzzy controller of uncertain nonlinear systems. IEEE Transactions on Fuzzy Systems 25 (6): 1601–1615.

    Article  Google Scholar 

  38. Lin, C.-M., T.-L. Le, and T.-T. Huynh. 2018. Self-evolving function-link interval type-2 fuzzy neural network for nonlinear system identification and control. Neurocomputing 275: 2239–2250.

    Article  Google Scholar 

  39. Hung, L.-C., and H.-Y. Chung. 2007. Decoupled sliding-mode with fuzzy-neural network controller for nonlinear systems. International Journal of Approximate Reasoning 46 (1): 74–97.

    Article  MathSciNet  Google Scholar 

  40. Hsu, C.-F. 2007. Self-organizing adaptive fuzzy neural control for a class of nonlinear systems. IEEE Transactions on Neural Networks 18 (4): 1232–1241.

    Article  Google Scholar 

  41. Liu, Y.-J., and S. Tong. 2014. Adaptive nn tracking control of uncertain nonlinear discrete-time systems with nonaffine dead-zone input. IEEE Transactions on Cybernetics 45 (3): 497–505.

    Article  Google Scholar 

  42. Fei, J., and T. Wang. 2019. Adaptive fuzzy-neural-network based on rbfnn control for active power filter. International Journal of Machine Learning and Cybernetics 10 (5): 1139–1150.

    Article  Google Scholar 

  43. Ge, S.S., J. Zhang, and T.H. Lee. 2004. Adaptive neural network control for a class of mimo nonlinear systems with disturbances in discrete-time. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics) 34 (4): 1630–1645.

    Article  Google Scholar 

  44. Liu, Y., L. Liu, and S. Tong. 2014. Adaptive neural network tracking design for a class of uncertain nonlinear discrete-time systems with dead-zone. Science China Information Sciences 57 (3): 1–12.

    Article  Google Scholar 

  45. Ge, S.S., C. Yang, and T.H. Lee. 2008. Adaptive predictive control using neural network for a class of pure-feedback systems in discrete time. IEEE Transactions on Neural Networks 19 (9): 1599–1614.

    Article  Google Scholar 

  46. Guangbin, C., D. Guangren, H. Changhua. 2010. On some classes of control-oriented model of air-breathing hypersonic vehicles. In: 2010 Chinese Control and Decision Conference, pp. 2955–2960, IEEE.

  47. Ataei-Esfahani, A., Q. Wang. 2007. Nonlinear control design of a hypersonic aircraft using sum-of-squares method. In: 2007 American Control Conference, pp. 5278–5283, IEEE.

  48. Xu, B., D. Yang, Z. Shi, Y. Pan, B. Chen, and F. Sun. 2017. Online recorded data-based composite neural control of strict-feedback systems with application to hypersonic flight dynamics. IEEE Transactions on Neural Networks and Learning Systems 29 (8): 3839–3849.

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported by MATRICS project Grant No. MTR/2021/000478 from 548 the Science and Engineering Research Board (SERB), India.

Author information

Authors and Affiliations

  1. Department of Mathematics, Lovely Professional University, Phagwara, Punjab, 144402, India

    Rahul Kumar

  2. Department of Mathematics, Central University of Jammu, Samba, J&K, 184311, India

    Uday Pratap Singh & Arun Bali

  3. School of Computing Science and Engineering, VIT Bhopal University, Sehore, MP, 466114, India

    Siddharth Singh Chouhan

  4. Department of Computer Science and Information Technology, Central University of Haryana, Jat, 123031, India

    Anoop Kumar Tiwari

Authors
  1. Rahul Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Uday Pratap Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Arun Bali
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Siddharth Singh Chouhan
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Anoop Kumar Tiwari
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Uday Pratap Singh.

Additional information

Communicated by S. Ponnusamy.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kumar, R., Singh, U.P., Bali, A. et al. Adaptive control of unknown fuzzy disturbance-based uncertain nonlinear systems: application to hypersonic flight dynamics. J Anal 32, 1395–1414 (2024). https://doi.org/10.1007/s41478-023-00687-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s41478-023-00687-z

Keywords

Mathematics Subject Classification

Search

Navigation