Parameter identification of nonlinear system using an improved Lozi map based chaotic optimization algorithm (ILCOA)

  • S. Mohammadreza Ebrahimi
  • Milad MalekzadehEmail author
  • Mojtaba Alizadeh
  • S. Hassan HosseinNia
Original Paper


In this paper, an efficient stochastic optimization algorithm is presented for parameter identification of nonlinear systems. Due to its robust performance, short running time and desirable potency to find local minimums the Lozi map-based chaotic optimization algorithm is an appropriate choice to estimate unknown parameters of nonlinear dynamic systems. To enhance the identification efficacy and in order to escape local minimum, a modified version of this algorithm with higher stability and better performance is rendered in this paper. An Improved Lozi map-based chaotic optimization algorithm (ILCOA) is employed to identify three nonlinear systems and the performance of the proposed algorithm is compared with other optimization algorithms. The simulation results of identification endorse the effectiveness of the proposed method.


Identification Stochastic optimization ILCOA Nonlinear systems 



  1. Acharjee P, Goswami SK (2010) Chaotic particle swarm optimization based robust load flow. Int J Electr Power Energy Syst 32(2):141–146CrossRefGoogle Scholar
  2. Angelov P, Yager R (2013) Density-based averaging—a new operator for data fusion. Inf Sci 222:163–174MathSciNetCrossRefzbMATHGoogle Scholar
  3. Angelov P, Ramezani R, Zhou X (2008) Autonomous novelty detection and object tracking in video streams using evolving clustering and Takagi-Sugeno type neuro-fuzzy system. In: IEEE international joint conference on neural networks, 2008. IJCNN 2008 (IEEE World Congress on Computational Intelligence). pp 1456–1463. IEEEGoogle Scholar
  4. Angelov P, Škrjanc I, Blažič S (2013) Robust evolving cloud-based controller for a hydraulic plant. In: 2013 IEEE conference on evolving and adaptive intelligent systems (EAIS), pp 1–8. IEEEGoogle Scholar
  5. Azami H, Malekzadeh M, Sanei S, Khosravi A (2012) Optimization of orthogonal polyphase coding waveform for MIMO radar based on evolutionary algorithms. J Math Comput Sci 6(2):146–153CrossRefGoogle Scholar
  6. Babu BC, Gurjar S (2014) A novel simplified two-diode model of photovoltaic (PV) module. IEEE J Photovolt 4(4):1156–1161CrossRefGoogle Scholar
  7. Billings SA, Jamaluddin HB, Chen S (1991) A comparison of the backpropagation and recursive prediction error algorithms for training neural networks. Mech Syst Signal Process 5(3):233–255CrossRefGoogle Scholar
  8. Bresler Y, Macovski A (1986) Exact maximum likelihood parameter estimation of superimposed exponential signals in noise. IEEE Trans Acoust Speech Signal Process 34(5):1081–1089CrossRefGoogle Scholar
  9. Chatterjee A, Ghoshal SP, Mukherjee V (2011) Chaotic ant swarm optimization for fuzzy-based tuning of power system stabilizer. Int J Electr Power Energy Syst 33(3):657–672CrossRefGoogle Scholar
  10. Chellaswamy C, Ramesh R (2016) Parameter extraction of solar cell models based on adaptive differential evolution algorithm. Renew Energy 97:823–837CrossRefGoogle Scholar
  11. Chen G, Ueta T (1999) Yet another chaotic attractor. Int J Bifur Chaos 9(07):1465–1466MathSciNetCrossRefzbMATHGoogle Scholar
  12. Chen S, Billings SA, Luo W (1989) Orthogonal least squares methods and their application to non-linear system identification. Int J Control 50(5):1873–1896CrossRefzbMATHGoogle Scholar
  13. Costa B, Skrjanc I, Blazic S, Angelov P (2013) A practical implementation of self-evolving cloud-based control of a pilot plant. In: 2013 IEEE international conference on cybernetics (CYBCONF), pp 7–12. IEEEGoogle Scholar
  14. dos Santos Coelho L (2009) Tuning of PID controller for an automatic regulator voltage system using chaotic optimization approach. Chaos Solitons Fractals 39(4):1504–1514CrossRefGoogle Scholar
  15. Farahani M, Ganjefar S, Alizadeh M (2012) PID controller adjustment using chaotic optimisation algorithm for multi-area load frequency control. IET Control Theory Appl 6(13):1984–1992MathSciNetCrossRefGoogle Scholar
  16. Gao X, Cui Y, Hu J, Xu G, Wang Z, Qu J, Wang H (2018) Parameter extraction of solar cell models using improved shuffled complex evolution algorithm. Energy Convers Manag 157:460–479CrossRefGoogle Scholar
  17. Godfrey KR, Jones P (1986) Signal processing for control, vol 79. Springer, BerlinCrossRefGoogle Scholar
  18. Gong W, Cai Z (2013) Parameter extraction of solar cell models using repaired adaptive differential evolution. Sol Energy 94:209–220CrossRefGoogle Scholar
  19. Hejri M, Mokhtari H, Azizian MR, Ghandhari M, Soder L (2014) On the parameter extraction of a five-parameter double-diode model of photovoltaic cells and modules. IEEE J Photovolt 4(3):915–923CrossRefGoogle Scholar
  20. Ishaque K, Salam Z, Taheri H (2011) Simple, fast and accurate two-diode model for photovoltaic modules. Solar Energy Mater Solar Cells 95(2):586–594CrossRefGoogle Scholar
  21. Jaleel EA, Aparna K (2018) Identification of realistic distillation column using hybrid particle swarm optimization and NARX based artificial neural network. Evol Syst 1–18Google Scholar
  22. Li X, Yin M (2014) Parameter estimation for chaotic systems by hybrid differential evolution algorithm and artificial bee colony algorithm. Nonlinear Dyn 77(1–2):61–71MathSciNetCrossRefGoogle Scholar
  23. Lorenz EN (1963) Deterministic nonperiodic flow. J Atmos Sci 20(2):130–141CrossRefzbMATHGoogle Scholar
  24. Malekzadeh M, Khosravi A, Alighale S, Azami H (2012) Optimization of orthogonal poly phase coding waveform based on bees algorithm and artificial bee colony for mimo radar. In: International conference on intelligent computing. Springer, Berlin, Heidelberg, pp 95–102Google Scholar
  25. Malekzadeh M, Sadati J, Alizadeh M (2016) Adaptive PID controller design for wing rock suppression using self-recurrent wavelet neural network identifier. Evol Syst 7(4):267–275CrossRefGoogle Scholar
  26. Malekzadeh M, Khosravi A, Tavan M (2018a) Observer based control scheme for DC-DC boost converter using sigma–delta modulator. COMPEL Int J Comput Math Electr Electron Eng 37(2):784–798CrossRefGoogle Scholar
  27. Malekzadeh M, Khosravi A, Tavan M (2018b) Immersion and invariance-based filtered transformation with application to estimator design for a class of DC–DC converters. Trans Inst Meas Control 0142331218777563Google Scholar
  28. Mendel E, Krohling RA, Campos M (2011) Swarm algorithms with chaotic jumps applied to noisy optimization problems. Inf Sci 181(20):4494–4514MathSciNetCrossRefzbMATHGoogle Scholar
  29. Niu Q, Zhang H, Li K (2014) An improved TLBO with elite strategy for parameters identification of PEM fuel cell and solar cell models. Int J Hydrogen Energy 39(8):3837–3854CrossRefGoogle Scholar
  30. Sadeghi-Tehran P, Cara AB, Angelov P, Pomares H, Rojas I, Prieto A (2012) Self-evolving parameter-free rule-based controller. In 2012 IEEE international conference on fuzzy systems (FUZZ-IEEE), pp 1–8. IEEEGoogle Scholar
  31. Salahshour E, Malekzadeh M, Gordillo F, Ghasemi J (2018a) Quantum neural network-based intelligent controller design for CSTR using modified particle swarm optimization algorithm. Trans Inst Meas Control 0142331218764566Google Scholar
  32. Salahshour E, Malekzadeh M, Gholipour R, Khorashadizadeh S (2018b) Designing multi-layer quantum neural network controller for chaos control of rod-type plasma torch system using improved particle swarm optimization. Evol Syst 1–15Google Scholar
  33. Tavazoei MS, Haeri M (2007) Comparison of different one-dimensional maps as chaotic search pattern in chaos optimization algorithms. Appl Math Comput 187(2):1076–1085MathSciNetzbMATHGoogle Scholar
  34. Ursem RK, Vadstrup P (2004) Parameter identification of induction motors using stochastic optimization algorithms. Appl Soft Comput 4(1):49–64CrossRefGoogle Scholar
  35. Wang,J.,Chen,X.andFu,J., 2014.Adaptive finite-time control of chaos in permanent magnet synchronous motor with uncertain parameters.Nonlinear Dyn 78(2):1321–1328CrossRefzbMATHGoogle Scholar
  36. Xiong G, Zhang J, Shi D, He Y (2018) Parameter extraction of solar photovoltaic models using an improved whale optimization algorithm. Energy Convers Manag 174:388–405CrossRefGoogle Scholar
  37. Xu S, Wang Y (2017) Parameter estimation of photovoltaic modules using a hybrid flower pollination algorithm. Energy Convers Manag 144:53–68CrossRefGoogle Scholar
  38. Zheng YX, Liao Y (2016) Parameter identification of nonlinear dynamic systems using an improved particle swarm optimization. Optik-Int J Light Electron Opt 127(19):7865–7874CrossRefGoogle Scholar
  39. Zhou X, Angelov P, 2007, April. Autonomous visual self-localization in completely unknown environment using evolving fuzzy rule-based classifier. In: IEEE Symposium on computational intelligence in security and defense applications, 2007. CISDA 2007, pp 131–138. IEEEGoogle Scholar
  40. Zhou CS, Chen TL (2000) Chaotic neural networks and chaotic annealing. Neurocomputing 30(1–4):293–300CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • S. Mohammadreza Ebrahimi
    • 1
  • Milad Malekzadeh
    • 1
    Email author
  • Mojtaba Alizadeh
    • 2
  • S. Hassan HosseinNia
    • 3
  1. 1.Faculty of Electrical EngineeringBabol Noshirvani University of TechnologyBabolIran
  2. 2.Faculty of Electrical EngineeringK.N. Toosi University of TechnologyTehranIran
  3. 3.Department of Precision and Microsystems EngineeringDelft University of TechnologyDelftThe Netherlands

Personalised recommendations