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Brain-inspired STA for parameter estimation of fractional-order memristor-based chaotic systems

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Abstract

It is very important to estimate the unknown parameters of the fractional-order memristor-based chaotic systems (FOMCSs). In this study, a brain-inspired state transition algorithm (BISTA) is proposed to estimate the parameters of the FOMCSs. In order to generate a better initial population, a novel initialization approach based on opposition-based learning is presented. To balance the global search and local search, and accelerate the convergence speed, the mutual learning and selective learning are proposed in the optimization process. The performance of the proposed algorithm is comprehensively evaluated on two typical FOMCSs. The simulation results and statistical analysis have demonstrated the effectiveness of the proposed algorithm. For the fractional-order memristor-based Lorenz system, the proposed method can increase the estimated value of parameters by at least one order of magnitude compared with the other methods.

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References

  1. Zhao Y, Zhang W, Su H, Yang J (2018) Observer-based synchronization of chaotic systems satisfying incremental quadratic constraints and its application in secure communication. IEEE Transactions on Systems Man, and Cybernetics: Systems 50(12):5221–5232

    Article  Google Scholar 

  2. Wu X, Shen S (2009) Chaos in the fractional-order lorenz system. Int J Comput Math 86 (7):1274–1282

    Article  MathSciNet  MATH  Google Scholar 

  3. Zhang W, Zhou S, Li H, Zhu H (2009) Chaos in a fractional-order rössler system. Chaos, Solitons & Fractals 42(3):1684–1691

    Article  MATH  Google Scholar 

  4. Li C, Chen G (2004) Chaos in the fractional order chen system and its control. Chaos, Solitons & Fractals 22(3):549–554

    Article  MATH  Google Scholar 

  5. Chua L (1971) Memristor-the missing circuit element. IEEE Transactions on Circuit Theory 18 (5):507–519

    Article  Google Scholar 

  6. Khalid M (2019) Review on various memristor models, characteristics, potential applications, and future works. Trans Electr Electron Mater 20(4):289–298

    Article  Google Scholar 

  7. Petras I (2010) Fractional-order memristor-based chua’s circuit. IEEE Trans Circuits Syst II Express Briefs 57(12):975–979

    Google Scholar 

  8. Cafagna D, Grassi G (2012) On the simplest fractional-order memristor-based chaotic system. Nonlinear Dyn 70(2):1185–1197

    Article  MathSciNet  Google Scholar 

  9. Teng L, Iu HH, Wang X, Wang X (2014) Chaotic behavior in fractional-order memristor-based simplest chaotic circuit using fourth degree polynomial. Nonlinear Dyn 77(1):231–241

    Article  Google Scholar 

  10. Huang X, Jia J, Li Y, Wang Z (2016) Complex nonlinear dynamics in fractional and integer order memristor-based systems. Neurocomputing 218:296–306

    Article  Google Scholar 

  11. Xi H, Li Y, Huang X (2014) Generation and nonlinear dynamical analyses of fractional-order memristor-based lorenz systems. Entropy 16(12):6240–6253

    Article  Google Scholar 

  12. Gu Y, Wang H, Yu Y (2020) Synchronization for commensurate riemann-liouville fractional-order memristor-based neural networks with unknown parameters. J Frankl Inst 357(13):8870–8898

    Article  MathSciNet  MATH  Google Scholar 

  13. Liu H, Chi J, Li Z, Zeng Z, Lü J. (2021) Parameter identification of memristor-based chaotic systems via the drive-response synchronization method. IEEE Trans Circuits Syst II Express Briefs 68 (6):2082–2086

    Google Scholar 

  14. Gu Y, Yu Y, Wang H (2017) Synchronization-based parameter estimation of fractional-order neural networks. Physica A 483:351–361

    Article  MathSciNet  MATH  Google Scholar 

  15. Lei Z, Gao S, Zhang Z, Zhou M, Cheng J (2022) Mo4: a many-objective evolutionary algorithm for protein structure prediction. IEEE Trans Evol Comput 26(3):417–430

    Article  Google Scholar 

  16. Li K, Chen R, Fu G, Yao X (2019) Two-archive evolutionary algorithm for constrained multiobjective optimization. IEEE Trans Evol Comput 23(2):303–315

    Article  Google Scholar 

  17. Camacho-Villalón CL, Dorigo M, Stützle T (2022) Pso-x: a component-based framework for the automatic design of particle swarm optimization algorithms. IEEE Trans Evol Comput 26(3):402–416

    Article  Google Scholar 

  18. Wang G-G, Deb S, Cui Z (2019) Monarch butterfly optimization. Neural Comput Appl 31 (7):1995–2014

    Article  Google Scholar 

  19. Wang G-G (2018) Moth search algorithm: a bio-inspired metaheuristic algorithm for global optimization problems. Memetic Computing 10(2):151–164

    Article  Google Scholar 

  20. Yang Y, Chen H, Heidari AA, Gandomi AH (2021) Hunger games search: visions, conception, implementation, deep analysis, perspectives, and towards performance shifts. Expert Syst Appl 177:114864

    Article  Google Scholar 

  21. Ahmadianfar I, Heidari AA, Gandomi AH, Chu X, Chen H (2021) Run beyond the metaphor: an efficient optimization algorithm based on runge kutta method. Expert Syst Appl 181:115079

    Article  Google Scholar 

  22. Houssein EH, Helmy BE-D, Rezk H, Nassef AM (2021) An enhanced archimedes optimization algorithm based on local escaping operator and orthogonal learning for pem fuel cell parameter identification. Eng Appl Artif Intell 103:104309

    Article  Google Scholar 

  23. Peng Y, He S, Sun K (2022) Parameter identification for discrete memristive chaotic map using adaptive differential evolution algorithm. Nonlinear Dyn 107(1):1263–1275

    Article  Google Scholar 

  24. Fathy A, Elaziz MA, Sayed ET, Olabi AG, Rezk H (2019) Optimal parameter identification of triple-junction photovoltaic panel based on enhanced moth search algorithm. Energy 188:116025

    Article  Google Scholar 

  25. Zhou X, Yang C, Gui W (2012) State transition algorithm. Journal of Industrial and Management Optimization 8(4):1039–1056

    Article  MathSciNet  MATH  Google Scholar 

  26. Zhou X, Gao Y, Li C, Huang Z (2022) A multiple gradient descent design for multi-task learning on edge computing: multi-objective machine learning approach. IEEE Transactions on Network Science and Engineering 9(1):121–133

    Article  MathSciNet  Google Scholar 

  27. Huang Z, Yang C, Zhou X, Gui W (2018) A novel cognitively inspired state transition algorithm for solving the linear bi-level programming problem. Cogn Comput 10(5):816–826

    Article  Google Scholar 

  28. Huang Z, Yang C, Zhou X, Yang S (2020) Energy consumption forecasting for the nonferrous metallurgy industry using hybrid support vector regression with an adaptive state transition algorithm. Cogn Comput 12(2):357–368

    Article  Google Scholar 

  29. Huang Z, Yang C, Chen X, Zhou X, Chen G, Huang T, Gui W (2021) Functional deep echo state network improved by a bi-level optimization approach for multivariate time series classification. Appl Soft Comput 106:107314

    Article  Google Scholar 

  30. Huang Z, Yang C, Zhou X, Huang T (2018) A hybrid feature selection method based on binary state transition algorithm and relieff. IEEE J Biomed Health Inform 23(5):1888–1898

    Article  Google Scholar 

  31. Huang Z, Yang C, Chen X, Huang K, Xie Y (2020) Adaptive over-sampling method for classification with application to imbalanced datasets in aluminum electrolysis. Neural Comput Appl 32(11):7183–7199

    Article  Google Scholar 

  32. Zhou X, Yang C, Gui W (2018) A statistical study on parameter selection of operators in continuous state transition algorithm. IEEE Transactions on Cybernetics 49(10):3722–3730

    Article  Google Scholar 

  33. Zhou X, Tian J, Wang Z, Yang C, Huang T, Xu X (2022) Nonlinear bilevel programming approach for decentralized supply chain using a hybrid state transition algorithm. Knowledge-based Systems 108119

  34. Han J, Yang C, Lim C. -C., Zhou X, Shi P (2022) Stackelberg game approach for robust optimization with fuzzy variables. IEEE Trans Fuzzy Syst 30(1):258–269

    Article  Google Scholar 

  35. Pierezan J, Dos Santos Coelho L (2018) Coyote optimization algorithm: a new metaheuristic for global optimization problems. In: 2018 IEEE Congress on evolutionary computation (CEC), pp 1–8

  36. Hansen N, Müller SD, Koumoutsakos P (2003) Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (cma-es). Evol Comput 11(1):1–18

    Article  Google Scholar 

  37. Ahmadianfar I, Bozorg-Haddad O, Chu X (2020) Gradient-based optimizer: a new metaheuristic optimization algorithm. Inf Sci 540:131–159

    Article  MathSciNet  MATH  Google Scholar 

  38. Tanabe R, Fukunaga AS (2014) Improving the search performance of shade using linear population size reduction

  39. Brest J, Maučec MS, Bošković B (2017) Single objective real-parameter optimization: Algorithm jso. In: 2017 IEEE Congress on evolutionary computation (CEC), pp 1311–1318

  40. Kumar A, Misra RK, Singh D (2017) Improving the local search capability of effective butterfly optimizer using covariance matrix adapted retreat phase. In: 2017 IEEE Congress on evolutionary computation (CEC), pp 1835–1842

  41. Sun X, Shi Z, Zhu J (2021) Multiobjective design optimization of an ipmsm for evs based on fuzzy method and sequential taguchi method. IEEE Trans Ind Electron 68(11):10592–10600

    Article  Google Scholar 

  42. Rakkiyappan R, Sivasamy R, Park JH (2014) Synchronization of fractional-order different memristor-based chaotic systems using active control. Can J Phys 92(12):1688–1695

    Article  Google Scholar 

  43. Carrasco J, García S, Rueda MM, Das S, Herrera F (2020) Recent trends in the use of statistical tests for comparing swarm and evolutionary computing algorithms: Practical guidelines and a critical review. Swarm Evol Comput 54:100665

    Article  Google Scholar 

Download references

Acknowledgements

The authors thank the National Natural Science Foundation of China (Grant Nos. 62103444 and 62273357), and the Hunan Provincial Natural Science Foundation of China (Grant No. 2021JJ20082) for their funding support.

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    Authors and Affiliations

    1. School of Automation, Central South University, Changsha, 410083, Hunan, China

      Zhaoke Huang, Chunhua Yang, Xiaojun Zhou & Weihua Gui

    2. Peng Cheng Laboratory, Shenzhen, 518000, Guangdong, China

      Zhaoke Huang & Xiaojun Zhou

    3. Texas A&M University at Qatar, Doha, 23874, Qatar

      Tingwen Huang

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    1. Zhaoke Huang
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    2. Chunhua Yang
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    Correspondence to Zhaoke Huang.

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    Chunhua Yang, Xiaojun Zhou, Weihua Gui and Tingwen Huang are contributed equally to this work.

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    Huang, Z., Yang, C., Zhou, X. et al. Brain-inspired STA for parameter estimation of fractional-order memristor-based chaotic systems. Appl Intell 53, 18653–18665 (2023). https://doi.org/10.1007/s10489-022-04435-x

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