Skip to main content
SpringerLink
Log in

Deep learning controller for nonlinear system based on Lyapunov stability criterion

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

Abstract

For the current paper, the technique of feed-forward neural network deep learning controller (FFNNDLC) for the nonlinear systems is proposed. The FFNNDLC combines the features of the multilayer feed-forward neural network (FFNN) and restricted Boltzmann machine (RBM). The RBM is a very important part for the deep learning controller, and it is applied in order to initialize a multilayer FFNN by performing unsupervised pretraining, where all the weights are equally zero. The weight laws for the proposed network are developed by Lyapunov stability method. The proposed controller is mainly compared with FFNN controller (FFNNC) and other controllers, where all the weights values for all the designed controllers are equally zero. The proposed FFNNDLC is able to respond the effect of the system uncertainties and external disturbances compared with other existing schemes as shown in simulation results section. To show the ability of the proposed controller to deal with a real system, it is implemented practically using an ARDUNIO DUE kit microcontroller for controlling an electromechanical system. It is proved that the proposed FFNNDLC is faster than other FFNNCs in which the parameters are learned using the backpropagation method. Besides, it is able to deal with the changes in both the disturbance and the system parameters.

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
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25

Similar content being viewed by others

References

  1. Khater AA, El-Bardini M, El-Rabaie NM (2015) Embedded adaptive fuzzy controller based on reinforcement learning for dc motor with flexible shaft. Arab J Sci Eng 40:2389–2406

    MATH  Google Scholar 

  2. Kumar R, Srivastava S, Gupta JRP, Mohindru A (2018) Diagonal recurrent neural network based identification of nonlinear dynamical systems with Lyapunov stability based adaptive learning rates. Neurocomputing 287:102–117

    Google Scholar 

  3. Guclu R, Gulez K (2008) Neural network control of seat vibrations of a non-linear full vehicle model using PMSM. Math Comput Modell 47:1356–1371

    MATH  Google Scholar 

  4. Zaki AM, El-Bardini M, Soliman FAS, Sharaf MM (2018) Embedded two level direct adaptive fuzzy controller for DC motor speed control. Ain Shams Eng J 9:65–75

    Google Scholar 

  5. Chang WD, Shih SP (2010) PID controller design of nonlinear systems using an improved particle swarm optimization approach. Commun Nonlinear Sci Numerl Simul 15:3632–3639

    MATH  Google Scholar 

  6. Khater AA, El-Nagar AM, El-Bardini M, El-Rabaie NM (2018) Adaptive T-S fuzzy controller using reinforcement learning based on Lyapunov stability. J Frankl Inst 355:6390–6415

    MathSciNet  MATH  Google Scholar 

  7. Shang C, Yang F, Huang D, Lyu W (2014) Data-driven soft sensor development based on deep learning technique. J Process Control 24:223–233

    Google Scholar 

  8. Zuo R, Xiong Y, Wang J, Carranza EJM (2019) Deep learning and its application in geochemical mapping. Earth-Sci Rev 192:1–14

    Google Scholar 

  9. Liu W, Wang Z, Liu X, Zeng N, Liu Y, Alsaadi FE (2017) A survey of deep neural network architectures and their applications. Neurocomputing 234:11–26

    Google Scholar 

  10. Qiao J, Wang G, Li X, Li W (2018) A self-organizing deep belief network for nonlinear system modeling. Appl Soft Comput 65:170–183

    Google Scholar 

  11. Sutar MK, Pattnaik S, Rana J (2015) Neural based controller for smart detection of crack in cracked cantilever beam. Mater Today Proc 2:2648–2653

    Google Scholar 

  12. Medjber A, Guessoum A, Belmili H, Mellit A (2016) New neural network and fuzzy logic controllers to monitor maximum power for wind energy conversion system. Energy 106:137–146. https://doi.org/10.1016/j.energy.2016.03.026

    Article  Google Scholar 

  13. Rajan S, Sahadev S (2016) Performance improvement of fuzzy logic controller using neural network. Procedia Technol 24:704–714

    Google Scholar 

  14. Farahani M, Ganjefar S (2015) An online trained fuzzy neural network controller to improve stability of power systems. Neurocomputing 162:245–255

    Google Scholar 

  15. da Silva Ribeiro VDJ, de Moraes Oliveira GF, Cristian M, Martins AL, Fernandes LD, Vega MP (2019) Neural network based controllers for the oil well drilling process. J Pet Sci Eng 176:573–583

    Google Scholar 

  16. Kumar R, Srivastava S, Gupta JRP (2017) Diagonal recurrent neural network based adaptive control of nonlinear dynamical systems using lyapunov stability criterion. ISA Trans 67:407–427

    Google Scholar 

  17. Zaineb BM, Aicha A, Mouna BH, Lassaad S (2017) Speed control of DC motor based on an adaptive feed forward neural IMC controller. In: 2017 International conference on green energy conversion systems (GECS), pp 1–7

  18. Nasr MB, Chtourou M (2014) Neural network control of nonlinear dynamic systems using hybrid algorithm. Appl Soft Comput 24:423–431

    Google Scholar 

  19. Cai Z, Zhang B, Yu X (2017) Neural network delayed control of an idealized offshore steel jacket platform. In: 2017 Eighth international conference on intelligent control and information processing (ICICIP). IEEE, pp 282–286

  20. Shafiq MA (2016). Direct adaptive inverse control of nonlinear plants using neural networks. In: 2016 Future Technologies Conference (FTC). IEEE, pp 827–830

  21. Son NN, Van Kien C, Anh HPH (2017) A novel adaptive feed-forward-PID controller of a SCARA parallel robot using pneumatic artificial muscle actuator based on neural network and modified differential evolution algorithm. Robot Auton Syst 96:65–80

    Google Scholar 

  22. Upadhyay D, Tarun N, Nayak T (2013) ANN based intelligent controller for inverted pendulum system. In: 2013 students conference on engineering and systems (SCES). IEEE, pp 1–6

  23. Chen J, Huang TC (2004) Applying neural networks to on-line updated PID controllers for nonlinear process control. J Process Control 14:211–230

    Google Scholar 

  24. Litjens G, Kooi T, Bejnordi BE et al (2017) A survey on deep learning in medical image analysis. Med Image Anal 42:60–88

    Google Scholar 

  25. Yuan J, Hou X, Xiao Y, Cao D, Guan W, Nie L (2019) Multi-criteria active deep learning for image classification. Knowledge-Based Syst 172:86–94

    Google Scholar 

  26. Mohanty SP, Hughes DP, Salathé M (2016) Using deep learning for image- based plant disease detection. Front Plant Sci 7:14–19

    Google Scholar 

  27. Altan G, Kutlu Y, Pekmezci AÖ, Nural S (2018) Deep learning with 3D-second order difference plot on respiratory sounds. Biomed Signal Process Control 45:58–69

    Google Scholar 

  28. Chatterjee A, Gupta U, Chinnakotla MK, Srikanth R, Galley M, Agrawal P (2019) Understanding emotions in text using deep learning and big data. Comput Human Behav 93:309–317

    Google Scholar 

  29. Jin X, Shao J, Zhang X, An W, Malekian R (2016) Modeling of nonlinear system based on deep learning framework. Nonlinear Dyn 84:1327–1340

    MathSciNet  Google Scholar 

  30. De la Rosa E, Yu W (2016) Randomized algorithms for nonlinear system identification with deep learning modification. Inf Sci 364:197–212

    MATH  Google Scholar 

  31. Qiao J, Wang G, Li W, Li X (2018) A deep belief network with PLSR for nonlinear system modeling. Neural Netw 104:68–79

    MATH  Google Scholar 

  32. Zhang K, Zheng L, Liu Z, Jia N (2019) A deep learning based multitask model for network-wide traffic speed predication. Neurocomputing 396:438–450

    Google Scholar 

  33. Krüger J, Lehr J, Schlüter M, Bischoff N (2019) Deep learning for part identification based on inherent features. CIRP Ann 68:9–12

    Google Scholar 

  34. Saba L, Biswas M, Kuppili V et al (2019) The present and future of deep learning in radiology. Eur J Radiol 114:14–24

    Google Scholar 

  35. Lyu Y, Chen J, Song Z (2019) Image-based process monitoring using deep learning framework. Chemom Intell Lab Syst 189:8–17

    Google Scholar 

  36. McBee MP, Awan OA, Colucci AT et al (2018) Deep learning in radiology. Acad Radiol 25:1472–1480

    Google Scholar 

  37. Zhu Z, Albadawy E, Saha A, Zhang J, Harowicz MR, Mazurowski MA (2019) Deep Learning for identifying radiogenomic associations in breast cancer. Comput Biol Med 109:85–90

    Google Scholar 

  38. Hinton GE (2012) A practical guide to training restricted Boltzmann machines. Neural networks: tricks of the trade. Springer, Berlin, pp 599–619

    Google Scholar 

  39. Golovko V, Kroshchanka A, Turchenko V, Jankowski S, Treadwell D (2015) A new technique for restricted Boltzmann machine learning. In: 2015 IEEE 8th international conference on intelligent data acquisition and advanced computing systems: technology and applications (IDAACS) (Vol. 1, pp. 182–186)

  40. Golovko V, Kroshchanka A, Treadwell D (2016) The nature of unsupervised learning in deep neural networks: a new understanding and novel approach. Opt Memory Neural Netw 25:127–141

    Google Scholar 

  41. Hinton GE (2002) Training products of experts by minimizing contrastive divergence. Neural Comput 14:1771–1800

    MATH  Google Scholar 

  42. Tieleman T (2008) Training restricted Boltzmann machines using approximations to the likelihood gradient. In: Proceedings of the 25th international conference on Machine learning (pp. 1064–1071)

  43. Heaton, J (2015) Artificial Intelligence for Humans, Volume 3: Neural Networks and Deep Learning. Heaton Research

  44. Erhan D, Bengio Y, Courville A et al (2010) Why does unsupervised pre-training help deep learning? J Mach Learn Res 11:625–660

    MathSciNet  MATH  Google Scholar 

  45. Ahn IS, Lan JH (1995) Implementation of a neural network controller and estimator using a digital signal processing chip. Math Comput Model 21:133–141

    MathSciNet  Google Scholar 

  46. Marini F, Magrì AL, Bucci R (2007) Multilayer feed-forward artificial neural networks for class modeling. Chemom Intell Lab Syst 88:118–124

    Google Scholar 

  47. Fourati F, Chtourou M (2007) A greenhouse control with feed-forward and recurrent neural networks. Simul Modell Pract Theory 15:1016–1028

    Google Scholar 

  48. Aftab MS, Shafiq M, Yousef H (2015) Lyapunov stability criterion based neural inverse tracking for unknown dynamic plants. In: 2015 IEEE international conference on industrial technology (ICIT) (pp. 321–325)

  49. Behera L, Kumar S, Patnaik A (2006) On adaptive learning rate that guarantees convergence in feed forward networks. IEEE Trans Neural Netw 17:1116–1125

    Google Scholar 

  50. Khater AA, El-Nagar AM, El-Bardini M, El-Rabaie NM (2019) Online learning based on adaptive learning rate for a class of recurrent fuzzy neural network. Neural Comput Appl. https://doi.org/10.1007/s00521-019-04372-w

    Article  MATH  Google Scholar 

  51. Khater AA., El-Nagar AM, El-Bardini M El-Rabaie N (2019) A novel structure of actor-critic learning based on an interval Type-2 TSK fuzzy neural network. IEEE Trans Fuzzy Syst

  52. Narendra KS, Parthasarathy K (1990) Identification and control of dynamical systems using neural networks. IEEE Trans Neural Netw 1:4–27

    Google Scholar 

  53. Kayacan E, Kayacan E, Khanesar MA (2014) Identification of nonlinear dynamic systems using type-2 fuzzy neural networks—A novel learning algorithm and a comparative study. IEEE Trans Indus Electr 62:1716–1724

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Industrial Electronics and Control Engineering, Faculty of Electronic Engineering, Menoufia University, Menof, 32852, Egypt

    Ahmad M. Zaki, Ahmad M. El-Nagar & Mohammad El-Bardini

  2. Department of Electronics and Computers Engineering, Nuclear Materials Authority, 530, El-Maadi, Cairo, Egypt

    F. A. S. Soliman

Authors
  1. Ahmad M. Zaki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ahmad M. El-Nagar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mohammad El-Bardini
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. F. A. S. Soliman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ahmad M. El-Nagar.

Ethics declarations

Conflict of interest

There is no conflict of interest between the authors to publish this manuscript.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zaki, A.M., El-Nagar, A.M., El-Bardini, M. et al. Deep learning controller for nonlinear system based on Lyapunov stability criterion. Neural Comput & Applic 33, 1515–1531 (2021). https://doi.org/10.1007/s00521-020-05077-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-020-05077-1

Keywords

Search

Navigation