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Gradient evolution-based counter propagation network for approximation of noncanonical system

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Abstract

In this paper, gradient evolution-based counter propagation network (GE-CPN) is developed for approximation of noncanonical form of nonlinear system and compared with some existing neural networks. GE-CPN is a multilayer feed-forward neural network, in which initial weights are assigning by the minimization of fitness function, i.e., mean-square error (MSE). An important feature of GE-CPN networks is learning from input data of nonlinear systems with parametric uncertainties. Under the framework of nonlinear system approximation using soft computing method, a new method GE-CPN is used to approximate the noncanonical systems. Adaptive and robust control of noncanonical systems in the presence of parameterization of system dynamics is much difficult. GE-CPN is used for approximation of noncanonical nonlinear systems at relative degree of accuracy. This paper shows that it is necessary to reparameterize neural network model and that such reparameterization is helpful for approximation of noncanonical systems. To demonstrate the effectiveness of GE-CPN method, simulation has been carried out by four noncanonical nonlinear systems.

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References

  • Alfaro-Ponce M, Arguelles A, Chairez I (2014) Continuous neural identifier for certain nonlinear systems with time in the input signal. Neural Netw 60:53–66

    Article  MATH  Google Scholar 

  • Attaran SM, Yusof R, Selamat H (2016) A novel optimization algorithm based on epsilon constraint-RBF neural network for tuning PID controller in decoupled HVAC system. Appl Therm Eng 99:613–624

    Article  Google Scholar 

  • Bortoletti A, Flore CD, Fanelli S, Zellini P (2003) A new class of Quasi-Newtonian methods for optimal learning in MLP-networks. IEEE Trans Neural Netw 14:263–273

    Article  Google Scholar 

  • Chen M, Ge S, How B (2010) Robust adaptive neural network control for a class of uncertain MIMO nonlinear systems with input nonlinearities. IEEE Trans Neural Netw 21:796–812

    Article  Google Scholar 

  • Cui R, Guo J, Gao B (2013) Game theory-based negotiation for multiple robots task allocation. Robotica 31(6):923–934

    Article  Google Scholar 

  • Dorigo M, Di Caro G (1999) Ant colony optimization: a new meta-heuristic. In: Proceedings of the IEEE congress on evolutionary computation

  • Ge S, Wang C (2012) Uncertain chaotic system control via adaptive neural design. Int J Bifurc Chaos 12:1097–1109

    Article  MathSciNet  MATH  Google Scholar 

  • Ge SS, Hang CC, Lee TH, Zhang T (2001) Stable adaptive neural network control. Kluwer, Boston

    MATH  Google Scholar 

  • Ge SS, Yang CG, Lee TH (2008) Adaptive predictive control using neural network for a class of pure-feedback systems in discrete time. IEEE Trans Neural Netw 19(9):1599–1614

    Article  Google Scholar 

  • Hecht-Nielsen R (1987) Counter propagation networks. Appl Opt 26:4979–4984

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  • Huang GB, Chen L, Siew CK (2006) Universal approximation using incremental constructive feedforward networks with random hidden nodes. IEEE Trans Neural Netw 17(4):879–892

    Article  Google Scholar 

  • Irani R, Nasimi R (2011) Evolving neural network using real coded genetic algorithm for permeability estimation of reservoir. Expert Syst Appl 38(8):9862–9866

    Article  Google Scholar 

  • Kohonen T (2012) Self-organizing and associative memory, 3rd edn. Springer, New York. ISBN 0-387-51387-6

  • Kuo RJ, Zulvia FE (2015) The gradient evolution algorithm: a new metaheuristic. Inform Sci 316:246–265

    Article  MATH  Google Scholar 

  • Lera G, Pinzolas M (2002) Neighborhood based Levenberg–Marquardt algorithm for neural network training. IEEE Trans Neural Netw 13:1200–1203

    Article  Google Scholar 

  • Li HX, Deng H (2006) An approximate internal model-based neural control for unknown nonlinear discrete processes. IEEE Trans Neural Netw 17(3):659–670

    Article  Google Scholar 

  • Li ZJ, Su CY (2013) Neural-adaptive control of single-master multiple slaves teleoperation for coordinated multiple mobile manipulators with time-varying communication delays and input uncertainty. IEEE Trans Neural Netw Learn Syst 24(9):1400–1413

    Article  Google Scholar 

  • Li ZJ, Ding L, Gao H, Duan GR, Su CY (2013) Trilateral tele-operation of adaptive fuzzy force/motion control for nonlinear teleoperators with communication random delays. IEEE Trans Fuzzy Syst 21(4):610–623

    Article  Google Scholar 

  • Liu YJ, Tong S (2015) Adaptive NN tracking control of uncertain nonlinear discrete-time systems with non-affine dead-zone input. IEEE Trans Cybern 45(3):497–505

    Article  Google Scholar 

  • Liu DR, Javaherian H, Kovalenko O, Huang T (2008) Adaptive critic learning techniques for engine torque and air-fuel ratio control. IEEE Trans Syst Man Cybern B Cybern 38(4):988–993

    Article  Google Scholar 

  • Liu D, Wang D, Zhao D, Wei Q, Jin N (2012) Neural-network-based optimal control for a class of unknown discrete-time nonlinear systems using globalized dual heuristic programming. IEEE Trans Autom Sci Eng 9(3):628–634

    Article  Google Scholar 

  • Morin P, Samson C (1997) Time-varying exponential stabilization of a rigid spacecraft with two control torques. IEEE Trans Autom Control 42(4):528–534

    Article  MathSciNet  MATH  Google Scholar 

  • Mukhrjee A, Zhang J (2008) A reliable multi-objective control strategy for batch processes based on bootstrap aggregated neural network models. J Process Control 18(7–8):720–734

    Article  Google Scholar 

  • Park J, Sandberg IW (1991) Universal approximation using radial-basis function networks. Neural Comput 3:246–257

    Article  Google Scholar 

  • Poggio T, Girosi F (1990) Networks for approximation and learning. Proc IEEE 78:1481–1497

    Article  MATH  Google Scholar 

  • Rossomando FG, Soria C, Carelli R (2011) Autonomous mobile robots navigation using RBF neural compensator. Control Eng Pract 19(3):215–222

    Article  Google Scholar 

  • Sakhre V, Singh UP, Jain S (2017) FCPN approach for uncertain nonlinear dynamical system with unknown disturbance. Int J Fuzzy Syst 19(2):452–469. https://doi.org/10.1007/s40815-016-0145-5

    Article  MathSciNet  Google Scholar 

  • Singh UP, Jain S (2016) Modified chaotic bat algorithm-based counter propagation neural network for uncertain nonlinear discrete time system. Int J Comput Intell Appl 15(3):1650016. https://doi.org/10.1142/S1469026816500164

    Article  Google Scholar 

  • Singh UP, Jain S (2017) Optimization of neural network for nonlinear discrete time system using modified quaternion firefly algorithm: case study of Indian currency exchange rate prediction. Soft Comput. https://doi.org/10.1007/s00500-017-2522-x

    Google Scholar 

  • Subudhi B, Jena D (2011) A differential evolution based neural network approach to nonlinear system identification. Appl Soft Comput 11:861–871

    Article  Google Scholar 

  • Tao G (2003) Adaptive control design and analysis. Wiley, Hoboken

    Book  MATH  Google Scholar 

  • Wang Y, Zhang H, Wang Y (2006) Fuzzy adaptive control of stochastic nonlinear system with unknown virtual control gain function. Acta Autom Sin 32:170–178

    MathSciNet  Google Scholar 

  • Wang L, Liu Z, Chen CLP, Zhang Y, Lee S, Chen X (2013) Energy-efficient SVM learning control system for biped walking robots. IEEE Trans Neural Netw Learn Syst 24(5):2013

    Google Scholar 

  • Wang L, Zeng Y, Chen T (2015) Backpropagation neural network with adaptive differential evolution algorithm for time series forecasting. Expert Syst Appl 42:855–863

    Article  Google Scholar 

  • Wu D, Si S, Wu S, Wang R (2017a) Dynamic trust relationships aware data privacy protection in mobile crowd-sensing. IEEE Internet Things J. https://doi.org/10.1109/JIOT.2017.2768073

    Google Scholar 

  • Wu D, Zhang F, Wang H, Wang R (2017b) Security-oriented opportunistic data forwarding in mobile social networks. Future Gener Comput Syst. https://doi.org/10.1016/j.future.2017.07.028

    Google Scholar 

  • Zhai D, Lu A, Li J, Zhang Q (2015) Fault detection for singular switched linear systems with multiple time-varying delay in finite frequency domain. Int J Syst Sci 47(13):3232–3257

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang HG, Cai LL (2002) Decentralized nonlinear adaptive control of an HVAC system. IEEE Trans Syst Man Cybern C Appl Rev 32(4):493–498

    Article  Google Scholar 

  • Zhang JR, Zhang J, Lok TM, Lyu MR (2007) A hybrid particle swarm optimization-back-propagation algorithm for feed-forward neural network training. Appl Math Comput 185(2):1026–1037

    MATH  Google Scholar 

  • Zhang Y, Tao G, Chen M (2015) Relative degrees and adaptive feedback linearization control of T-S fuzzy systems. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2015.2412138

    Google Scholar 

  • Zhihong M, Wu HR, Palaniswami M (1998) An adaptive tracking controller using neural networks for a class of nonlinear systems. IEEE Trans Neural Netw 9(5):947–955

    Article  Google Scholar 

  • Zhou B, Zheng WX, Duan GR (2011) Stability and stabilization of discrete-time periodic linear systems with actuator saturation. Automatica 47(8):1813–1820

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Uday Pratap Singh.

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On behalf of other author’s I declare that we have no conflict of interest.

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

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Communicated by V. Loia.

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Singh, U.P., Jain, S., Tiwari, A. et al. Gradient evolution-based counter propagation network for approximation of noncanonical system. Soft Comput 23, 4955–4967 (2019). https://doi.org/10.1007/s00500-018-3160-7

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