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Comparative study of neural networks for dynamic nonlinear systems identification

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Abstract

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.

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References

  • Abdollahi F, Talebi HA, Patel RV (2006) Stable identification of nonlinear systems using neural networks: theory and experiments. IEEE/ASME Trans Mechatron 11(4):488–495

    Article  Google Scholar 

  • 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):568–581

    Article  Google Scholar 

  • Arqub OA (2017) Adaptation of reproducing kernel algorithm for solving fuzzy fredholm-volterra integrodifferential equations. Neural Comput Appl 28(7):1591–1610

    Article  Google Scholar 

  • 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):3283–3302

    Article  MATH  Google Scholar 

  • 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):7191–7206

    Article  MATH  Google Scholar 

  • Atencia M, Joya G, Sandoval F (2013) Identification of noisy dynamical systems with parameter estimation based on hopfield neural networks. Neurocomputing 121:14–24

    Article  Google Scholar 

  • 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):1187–1200

    Article  Google Scholar 

  • 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 3540–3545

  • 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):1051–1070

    Article  MATH  Google Scholar 

  • 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):151–161

    Article  Google Scholar 

  • 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 2562–2567

  • Efe MO, Kaynak O (1999) A comparative study of neural network structures in identification of nonlinear systems. Mechatronics 9(3):287–300

    Article  Google Scholar 

  • 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):23–34

    MathSciNet  Google Scholar 

  • 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)

  • 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 Syst

  • 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)

  • Gabrijel I, Dobnikar A (2003) On-line identification and reconstruction of finite automata with generalized recurrent neural networks. Neural Netw 16(1):101–120

    Article  MATH  Google Scholar 

  • Haykin S, Network N (2004) A comprehensive foundation. Neural Netw 2:2004

    Google Scholar 

  • Hecht-Nielsen R et al (1988) Theory of the backpropagation neural network. Neural Netw 1(Supplement–1):445–448

    Article  Google Scholar 

  • Hornik K, Stinchcombe M, White H (1989) Multilayer feedforward networks are universal approximators. Neural Netw 2(5):359–366

    Article  MATH  Google Scholar 

  • Jin L, Gupta MM (1999) Stable dynamic backpropagation learning in recurrent neural networks. IEEE Trans Neural Netw 10(6):1321–1334

    Article  Google Scholar 

  • 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 3485–3490

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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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 1–6

  • 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 243–249

  • 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 1–17

  • 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 407–415

  • Kumar R, Srivastava S, Gupta JRP (2017) Lyapunov stability-based control and identification of nonlinear dynamical systems using adaptive dynamic programming. Soft Comput, pp 1–16

  • 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 1–23

  • Lee C-H, Teng C-C (2000) Identification and control of dynamic systems using recurrent fuzzy neural networks. IEEE Trans Fuzzy Syst 8(4):349–366

    Article  Google Scholar 

  • Lilly JH (2011) Fuzzy control and identification. Wiley, Hoboken

    MATH  Google Scholar 

  • Lin C-M, Hsu C-F (2005) Recurrent-neural-network-based adaptive-backstepping control for induction servomotors. IEEE Trans Industr Electron 52(6):1677–1684

    Article  Google Scholar 

  • 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 196:1–13

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Narendra KS, Parthasarathy K (1991) Gradient methods for the optimization of dynamical systems containing neural networks. IEEE Trans Neural Netw 2(2):252–262

    Article  Google Scholar 

  • Pan Y, Wang J (2012) Model predictive control of unknown nonlinear dynamical systems based on recurrent neural networks. IEEE Trans Industr Electron 59(8):3089–3101

    Article  MathSciNet  Google Scholar 

  • Paul RP (1981) Robot manipulators: mathematics, programming, and control: the computer control of robot manipulators. Richard Paul, Los Angeles

    Google Scholar 

  • 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 36–40

  • Polycarpou MM (1996) Stable adaptive neural control scheme for nonlinear systems. IEEE Trans Autom Control 41(3):447–451

    Article  MathSciNet  MATH  Google Scholar 

  • 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 1477–1482

  • 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 586–591

  • Roudbari A, Saghafi F (2014) Intelligent modeling and identification of aircraft nonlinear flight. Chin J Aeronaut 27(4):759–771

    Article  Google Scholar 

  • Sadegh N (1993) A perceptron network for functional identification and control of nonlinear systems. IEEE Trans Neural Netw 4(6):982–988

    Article  Google Scholar 

  • Savran A (2007) Multifeedback-layer neural network. IEEE Trans Neural Netw 18(2):373–384

    Article  Google Scholar 

  • Sciavicco L, Siciliano B (2012) Modelling and control of robot manipulators. Springer, Berlin

    MATH  Google Scholar 

  • Shin YC (1994) Radial basis function neural network for approximation and estimation of nonlinear stochastic dynamic systems. IEEE Trans Neural Netw 5(4):594–603

    Article  Google Scholar 

  • Simon H (1994) Neural networks: a comprehensive foundation. Prentice Hall PTR, Upper Saddle River

    MATH  Google Scholar 

  • 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):43–50

    Article  Google Scholar 

  • 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):977–989

    Article  Google Scholar 

  • Srivastava S, Singh M, Hanmandlu M, Jha AN (2005) New fuzzy wavelet neural networks for system identification and control. Appl Soft Comput 6(1):1–17

    Article  Google Scholar 

  • Srivastava S, Singh M, Madasu VK, Hanmandlu M (2008) Choquet fuzzy integral based modeling of nonlinear system. Appl Soft Comput 8(2):839–848

    Article  Google Scholar 

  • Teeter J, Chow M-Y (1998) Application of functional link neural network to hvac thermal dynamic system identification. IEEE Trans Industr Electron 45(1):170–176

    Article  Google Scholar 

  • Wlas M, Krzeminski Z, Toliyat HA (2008) Neural-network-based parameter estimations of induction motors. IEEE Trans Industr Electron 55(4):1783–1794

    Article  Google Scholar 

  • 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 476–481

  • 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 571–575

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Authors and Affiliations

  1. Department of Instrumentation and Control Engineering, Bharati Vidyapeeth’s College of Engineering, A-4, Paschim Vihar, New Delhi, 110063, India

    Rajesh Kumar

  2. Division of Instrumentation and Control Engineering, Netaji Subhas Institute of Technology, Sector 3, Dwarka, New Delhi, 110078, India

    Smriti Srivastava & J. R. P. Gupta

  3. Department of Electronics and Communication Engineering, Indraprastha Institute of Information Technology, New Delhi, 110020, India

    Amit Mohindru

Authors
  1. Rajesh Kumar
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  2. Smriti Srivastava
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  3. J. R. P. Gupta
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  4. Amit Mohindru
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Correspondence to Rajesh Kumar.

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This study is not funded by any agency.

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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.

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Kumar, R., Srivastava, S., Gupta, J.R.P. et al. Comparative study of neural networks for dynamic nonlinear systems identification. Soft Comput 23, 101–114 (2019). https://doi.org/10.1007/s00500-018-3235-5

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