Soft Computing

, Volume 23, Issue 1, pp 101–114 | Cite as

Comparative study of neural networks for dynamic nonlinear systems identification

  • Rajesh KumarEmail author
  • Smriti Srivastava
  • J. R. P. Gupta
  • Amit Mohindru
Methodologies and Application


In this paper, a comparative study is performed to test the approximation ability of different neural network structures. It involves three neural networks multilayer feedforward neural network (MLFFNN), diagonal recurrent neural network (DRNN), and nonlinear autoregressive with exogenous inputs (NARX) neural network. Their robustness is also tested and compared when the system is subjected to parameter variations and disturbance signals. Further, dynamic back-propagation algorithm is used to update the parameters associated with these neural networks. Four dynamical systems of different complexities including motor-driven robotic link are considered on which the comparative study is performed. The simulation results show the superior performance of DRNN identification model over NARX and MLFFNN identification models.


Diagonal recurrent neural network NARX model Identification Multilayer feedforward neural network Robustness 


Compliance with Ethical Standards


This study is not funded by any agency.

Conflict of Interest

Rajesh Kumar declares that he has no conflict of interest. Smriti Srivastava declares that she has no conflict of interest. J.R.P Gupta declares that he has no conflict of interest. Amit Mohindru declares that he has no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


  1. Abdollahi F, Talebi HA, Patel RV (2006) Stable identification of nonlinear systems using neural networks: theory and experiments. IEEE/ASME Trans Mechatron 11(4):488–495Google Scholar
  2. Al Seyab RK, Cao Y (2008) Nonlinear system identification for predictive control using continuous time recurrent neural networks and automatic differentiation. J Process Control 18(6):568–581Google Scholar
  3. Arqub OA (2017) Adaptation of reproducing kernel algorithm for solving fuzzy fredholm-volterra integrodifferential equations. Neural Comput Appl 28(7):1591–1610Google Scholar
  4. Arqub OA, Mohammed AL-S, Momani S, Hayat T (2016) Numerical solutions of fuzzy differential equations using reproducing kernel hilbert space method. Soft Comput 20(8):3283–3302zbMATHGoogle Scholar
  5. Arqub OA, Al-Smadi M, Momani S, Hayat T (2017) Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems. Soft Comput 21(23):7191–7206zbMATHGoogle Scholar
  6. Atencia M, Joya G, Sandoval F (2013) Identification of noisy dynamical systems with parameter estimation based on hopfield neural networks. Neurocomputing 121:14–24Google Scholar
  7. Banakar A, Azeem MF (2012) Local recurrent sigmoidal-wavelet neurons in feed-forward neural network for forecasting of dynamic systems: Theory. Appl Soft Comput 12(3):1187–1200Google Scholar
  8. Baruch IS, Flores JM, Garrido R (2001) A fuzzy neural recurrent multi-model for systems identification and control. In: Control conference (ECC), 2001 European. IEEE, pp 3540–3545Google Scholar
  9. Chen S, Billings SA, Grant PM (1992) Recursive hybrid algorithm for non-linear system identification using radial basis function networks. Int J Control 55(5):1051–1070zbMATHGoogle Scholar
  10. Chow TWS, Fang Y (1998) A recurrent neural-network-based real-time learning control strategy applying to nonlinear systems with unknown dynamics. IEEE Trans Industr Electron 45(1):151–161Google Scholar
  11. de Jesús Rubio J, Yu W (2005) Dead-zone kalman filter algorithm for recurrent neural networks. In: Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC’05. 44th IEEE Conference on. IEEE, pp 2562–2567Google Scholar
  12. Efe MO, Kaynak O (1999) A comparative study of neural network structures in identification of nonlinear systems. Mechatronics 9(3):287–300Google Scholar
  13. Fahmi A, Abdullah S, Amin F, Ali A (2018) Weighted average rating (war) method for solving group decision making problem using triangular cubic fuzzy hybrid aggregation (tcfha). Punjab Univ J Math 50(1):23–34MathSciNetGoogle Scholar
  14. Fahmi A, Abdullah S, Amin F, Ahmed R, Ali A. Triangular cubic linguistic hesitant fuzzy aggregation operators and their application in group decision making. J Intell Fuzzy Syst, pp 1–15 (Preprint)Google Scholar
  15. Fahmi A, Abdullah S, Amin F, Ali A (2017) Precursor selection for sol–gel synthesis of titanium carbide nanopowders by a new cubic fuzzy multi-attribute group decision-making model. J Intell SystGoogle Scholar
  16. Fahmi A, Abdullah S, Amin F, Siddiqui N (2017) Aggregation operators on triangular cubic fuzzy numbers and its application to multi-criteria decision making problems. J Intell Fuzzy Syst, pp 1–15 (Preprint)Google Scholar
  17. Gabrijel I, Dobnikar A (2003) On-line identification and reconstruction of finite automata with generalized recurrent neural networks. Neural Netw 16(1):101–120zbMATHGoogle Scholar
  18. Haykin S, Network N (2004) A comprehensive foundation. Neural Netw 2:2004Google Scholar
  19. Hecht-Nielsen R et al (1988) Theory of the backpropagation neural network. Neural Netw 1(Supplement–1):445–448Google Scholar
  20. Hornik K, Stinchcombe M, White H (1989) Multilayer feedforward networks are universal approximators. Neural Netw 2(5):359–366zbMATHGoogle Scholar
  21. Jin L, Gupta MM (1999) Stable dynamic backpropagation learning in recurrent neural networks. IEEE Trans Neural Netw 10(6):1321–1334Google Scholar
  22. Ku C-C, Lee KY (1992) Diagonal recurrent neural network based control using adaptive learning rates. In: Proceedings of the 31st IEEE Conference on Decision and Control. IEEE, pp 3485–3490Google Scholar
  23. Kumar R, Srivastava S, Gupta JRP (2017) Modeling and adaptive control of nonlinear dynamical systems using radial basis function network. Soft Comput 21(15):4447–4463Google Scholar
  24. Kumar R, Srivastava S, Gupta JRP (2017) Diagonal recurrent neural network based adaptive control of nonlinear dynamical systems using lyapunov stability criterion. ISA Trans 67:407–427Google Scholar
  25. Kumar R, Srivastava S, Gupta JRP (2016) Artificial neural network based pid controller for online control of dynamical systems. In: IEEE international conference on, in power electronics, intelligent control and energy systems (ICPEICES). IEEE, pp 1–6Google Scholar
  26. Kumar R, Srivastava S, Gupta JRP (2016) Modeling and control of one-link robotic manipulator using neural network based pid controller. In: Advances in computing, communications and informatics (ICACCI), 2016 International conference on. IEEE, pp 243–249Google Scholar
  27. Kumar R, Srivastava S, Gupta JRP (2016) Online modeling and adaptive control of robotic manipulators using gaussian radial basis function networks. Neural Comput Appl, pp 1–17Google Scholar
  28. Kumar R, Srivastava S, Gupta JRP (2017) A soft computing approach for modeling of nonlinear dynamical systems. In Proceedings of the 5th international conference on frontiers in intelligent computing: theory and applications. Springer, pp 407–415Google Scholar
  29. Kumar R, Srivastava S, Gupta JRP (2017) Lyapunov stability-based control and identification of nonlinear dynamical systems using adaptive dynamic programming. Soft Comput, pp 1–16Google Scholar
  30. Kumar R, Srivastava S, Gupta JRP (2018) Comparative study of neural networks for control of nonlinear dynamical systems with lyapunov stability-based adaptive learning rates. Arabian J Sci Eng, pp 1–23Google Scholar
  31. Lee C-H, Teng C-C (2000) Identification and control of dynamic systems using recurrent fuzzy neural networks. IEEE Trans Fuzzy Syst 8(4):349–366Google Scholar
  32. Lilly JH (2011) Fuzzy control and identification. Wiley, HobokenzbMATHGoogle Scholar
  33. Lin C-M, Hsu C-F (2005) Recurrent-neural-network-based adaptive-backstepping control for induction servomotors. IEEE Trans Industr Electron 52(6):1677–1684Google Scholar
  34. Liu Y-C, Liu S-Y, Wang N (2016) Fully-tuned fuzzy neural network based robust adaptive tracking control of unmanned underwater vehicle with thruster dynamics. Neurocomputing 196:1–13Google Scholar
  35. Narendra KS, Parthasarathy K (1990) Identification and control of dynamical systems using neural networks. IEEE Trans Neural Networks 1(1):4–27Google Scholar
  36. Narendra KS, Parthasarathy K (1991) Gradient methods for the optimization of dynamical systems containing neural networks. IEEE Trans Neural Netw 2(2):252–262Google Scholar
  37. Pan Y, Wang J (2012) Model predictive control of unknown nonlinear dynamical systems based on recurrent neural networks. IEEE Trans Industr Electron 59(8):3089–3101MathSciNetGoogle Scholar
  38. Paul RP (1981) Robot manipulators: mathematics, programming, and control: the computer control of robot manipulators. Richard Paul, Los AngelesGoogle Scholar
  39. Polycarpou MM, Ioannou PA (1992) Modelling, identification and stable adaptive control of continuous-time nonlinear dynamical systems using neural networks. In: American Control Conference. IEEE, pp 36–40Google Scholar
  40. Polycarpou MM (1996) Stable adaptive neural control scheme for nonlinear systems. IEEE Trans Autom Control 41(3):447–451MathSciNetzbMATHGoogle Scholar
  41. Rajesh MV, Archana R, Unnikrishnan A, Gopikakaumari R (2009) Particle filter based neural network modeling of nonlinear systems for state space estimation. In: Control and Decision Conference, 2009. CCDC’09. IEEE, Chinese, pp 1477–1482Google Scholar
  42. Riedmiller M, Braun H (1993) A direct adaptive method for faster backpropagation learning: The rprop algorithm. In: Neural Networks, IEEE International Conference on. IEEE, pp 586–591Google Scholar
  43. Roudbari A, Saghafi F (2014) Intelligent modeling and identification of aircraft nonlinear flight. Chin J Aeronaut 27(4):759–771Google Scholar
  44. Sadegh N (1993) A perceptron network for functional identification and control of nonlinear systems. IEEE Trans Neural Netw 4(6):982–988Google Scholar
  45. Savran A (2007) Multifeedback-layer neural network. IEEE Trans Neural Netw 18(2):373–384Google Scholar
  46. Sciavicco L, Siciliano B (2012) Modelling and control of robot manipulators. Springer, BerlinzbMATHGoogle Scholar
  47. Shin YC (1994) Radial basis function neural network for approximation and estimation of nonlinear stochastic dynamic systems. IEEE Trans Neural Netw 5(4):594–603Google Scholar
  48. Simon H (1994) Neural networks: a comprehensive foundation. Prentice Hall PTR, Upper Saddle RiverzbMATHGoogle Scholar
  49. Singh M, Srivastava S, Gupta JRP, Handmandlu M (2007) Identification and control of a nonlinear system using neural networks by extracting the system dynamics. IETE J Res 53(1):43–50Google Scholar
  50. Singh M, Srivastava S, Hanmandlu M, Gupta JRP (2009) Type-2 fuzzy wavelet networks (t2fwn) for system identification using fuzzy differential and lyapunov stability algorithm. Appl Soft Comput 9(3):977–989Google Scholar
  51. Srivastava S, Singh M, Hanmandlu M, Jha AN (2005) New fuzzy wavelet neural networks for system identification and control. Appl Soft Comput 6(1):1–17Google Scholar
  52. Srivastava S, Singh M, Madasu VK, Hanmandlu M (2008) Choquet fuzzy integral based modeling of nonlinear system. Appl Soft Comput 8(2):839–848Google Scholar
  53. Teeter J, Chow M-Y (1998) Application of functional link neural network to hvac thermal dynamic system identification. IEEE Trans Industr Electron 45(1):170–176Google Scholar
  54. Wlas M, Krzeminski Z, Toliyat HA (2008) Neural-network-based parameter estimations of induction motors. IEEE Trans Industr Electron 55(4):1783–1794Google Scholar
  55. Yang G-B, Donath M (1988) Dynamic model of a one-link robot manipulator with both structural and joint flexibility. In: Robotics and Automation, 1988. Proceedings., 1988 IEEE International Conference on. IEEE, pp 476–481Google Scholar
  56. Zhu Y-Q, Xie W-F, Yao J (2006) Nonlinear system identification using genetic algorithm based recurrent neural networks. In Electrical and Computer Engineering, 2006. CCECE’06. Canadian Conference on. IEEE, pp 571–575Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Instrumentation and Control EngineeringBharati Vidyapeeth’s College of EngineeringNew DelhiIndia
  2. 2.Division of Instrumentation and Control EngineeringNetaji Subhas Institute of TechnologyNew DelhiIndia
  3. 3.Department of Electronics and Communication EngineeringIndraprastha Institute of Information TechnologyNew DelhiIndia

Personalised recommendations