Skip to main content

Advertisement

SpringerLink
Log in

Fuzzy-Evolution Computing Paradigm for Fractional Hammerstein Control Autoregressive Systems

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

In this study, a fuzzy-evolution computing paradigm is presented for parameter estimation of fractional Hammerstein control autoregressive (F-HCAR) systems by exploiting the knacks of global optimization strength of genetic algorithms (GAs). The definition of Grunwald–Letnikov fractional derivative is exploiting in standard HCAR system for the development of F-HCAR model. The system identification problem of F-HCAR model is constructed by defining a merit or fitness function using mean square error approximation between the actual and calculated parameters of F-HCAR models. The decision variables of F-HCAR models are determined by optimization of merit function with the knacks of global search with GAs for sundry scenarios on noiseless and noisy environment in the system dynamics. Comparison of results between estimated and predicted responses of F-HCAR systems endorsed the accurate, stable and robust performance fuzzy-evolutionary GAs. The statistical calculations for merit function on MSE, Nash–Sutcliffe efficiency and Theil inequality coefficient through cumulative distribution plots, boxplot illustrations, histograms and probability results of Weibull distribution further substantiated designed procedures of fuzzy evolutionary GAs for F-HCAR systems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Algorithm 1
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

Similar content being viewed by others

Data availability

There is no any data associated with the said manuscript.

References

  1. Catania, G., Sorrentino, S.: Analytical modelling and ex-perimental identification of viscoelastic mechanical systems. Springer 6, 403–416 (2013)

    MATH  Google Scholar 

  2. Paola, M.D., Pinnola, F.P., Zingales, M.: Fractional diferential equations and related exact mechanical models. Comput. Math. Appl. 66, 608–620 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  3. Mohammadzadeh, A., Castillo, O., Band, S.S., Mosavi, A.: A novel fractional-order multiple-model type-3 fuzzy control for nonlinear systems with unmodeled dynamics. Int. J. Fuzzy Syst. 1–19 (2021).

  4. Ha, S., Chen, L., Liu, H.: Adaptive Fuzzy variable structure control of fractional-order nonlinear systems with input nonlinearities. Int. J. Fuzzy Syst. 1–15 (2021).

  5. Cheng, Y., Li, Y., Yang, J.: Novel approach of obtaining dynamic multi-attribute weight for intuitionistic fuzzy environment based on fractional integrals. Int. J. Fuzzy Syst. 22(1), 242–256 (2020)

    Article  Google Scholar 

  6. Mathiyalagan, K., Sangeetha, G.: Second-order sliding mode control for nonlinear fractional-order systems. Appl. Math. Comput. 383, 125264 (2020)

    MathSciNet  MATH  Google Scholar 

  7. Abdelaty, A.M., Roshdy, M., Said, L.A., Radwan, A.G.: Numerical simulations and FPGA implementations of fractional-order systems based on product integration rules. IEEE Access 8, 102093–102105 (2020)

    Article  Google Scholar 

  8. Wang, R., YunNing, Z., Chen, Y., Chen, X., Lei, X.: Fuzzy neural network-based chaos synchronization for a class of fractional-order chaotic systems: an adaptive sliding mode control approach. Nonlinear Dyn. 100(2), 1275–1287 (2020)

    Article  MATH  Google Scholar 

  9. Tuan, H.T., Trinh, H.: A qualitative theory of time delay nonlinear fractional-order systems. SIAM J. Control. Optim. 58(3), 1491–1518 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  10. Song, S., Park, J.H., Zhang, B., Song, X.: Adaptive hybrid fuzzy output feedback control for fractional-order nonlinear systems with time-varying delays and input saturation. Appl. Math. Computat. 364, 124662 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  11. Yousri, D., Mirjalili, S.: Fractional-order cuckoo search algorithm for parameter identification of the fractional-order chaotic, chaotic with noise and hyper-chaotic financial systems. Eng. Appl. Artif. Intell. 92, 103662 (2020)

    Article  Google Scholar 

  12. Wang, J., Wei, Y., Liu, T., Li, A., Wang, Y.: Fully parametric identification for continuous time fractional order Hammerstein systems. J. Franklin Inst. 357(1), 651–666 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  13. Zhang, S., Liu, L., Chen, Y.Q., Xue, D.: Synthesised fractional-order PD controller design for fractional-order time-delay systems based on improved robust stability surface analysis. IET Control Theory Appl. 14(20), 3723–3730 (2020)

    Article  Google Scholar 

  14. Shahri, E.S.A., Alfi, A., Machado, J.T.: Lyapunov method for the stability analysis of uncertain fractional-order systems under input saturation. Appl. Math. Model. 81, 663–672 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  15. Martínez-Guerra, R., Meléndez-Vázquez, F., Trejo-Zúñiga, I.: Fault-tolerant Control and Diagnosis for Integer and Fractional-order Systems-Fundamentals of Fractional Calculus and Differential Algebra with Real-Time Applications, vol. 328, pp. 1–186. Springer, Berlin.

  16. Bingi, K., Ibrahim, R., Karsiti, M.N., Hassan, S.M., Harindran, V.R.: Fractional-Order Systems and PID Controllers. Springer, New York (2020).

  17. Martínez-Guerra, R., Meléndez-Vázquez, F., Trejo-Zúñiga, I.: Fault-tolerant Control and Diagnosis for Integer and Fractional-order Systems.

  18. Chakraverty, S., Jena, R.M., Jena, S.K.: Time-fractional order biological systems with uncertain parameters. Synth. Lect. Math. Stat. 12(1), 1–160 (2020)

    MATH  Google Scholar 

  19. Chaudhary, N.I., Raja, M.A.Z.: Design of fractional adaptive strategy for input nonlinear Box-Jenkins systems. Signal Process. 116, 141–151 (2015)

    Article  Google Scholar 

  20. Pu, Y.F., Zhou, J.L., Zhang, Y., Zhang, N., Huang, G., Siarry, P.: Fractional extreme value adaptive training method: fractional steepest descent approach. IEEE Trans. Neural Netw. Learn. Syst. 26(4), 653–662 (2013)

    Article  MathSciNet  Google Scholar 

  21. Zubair, S., Chaudhary, N.I., Khan, Z.A., Wang, W.: Momentum fractional LMS for power signal parameter estimation. Signal Process. 142, 441–449 (2018)

    Article  Google Scholar 

  22. Geravanchizadeh, M., Ghalami Osgouei, S.: Speech enhancement by modified convex combination of fractional adaptive filtering. Iran. J. Electric. Electron. Eng. 10(4), 256–266 (2014)

    Google Scholar 

  23. Chaudhary, N.I., Raja, M.A.Z., Khan, A.U.R.: Design of modified fractional adaptive strategies for Hammerstein nonlinear control autoregressive systems. Nonlinear Dyn. 82(4), 1811–1830 (2015)

    Article  MATH  Google Scholar 

  24. Chaudhary, N.I., Zubair, S., Raja, M.A.Z., Dedovic, N.: Normalized fractional adaptive methods for nonlinear control autoregressive systems. Appl. Math. Model. 66, 457–471 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  25. Aslam, M.S., Raja, M.A.Z.: A new adaptive strategy to improve online secondary path modeling in active noise control systems using fractional signal processing approach. Signal Process. 107, 433–443 (2015)

    Article  Google Scholar 

  26. Gogineni, V.C., Talebi, S.P., Werner, S., Mandic, D.P.: Fractional-order correntropy adaptive filters for distributed processing of $\alpha $-stable signals. IEEE Signal Process. Lett. 27, 1884–1888 (2020)

  27. Shezaf, N., Abramov-Segal, H., Sutskover, I., Bar-Sella, R.: Adaptive low complexity algorithm for image zooming at fractional scaling ratio. In: 21st IEEE Convention of the Electrical and Electronic Engineers in Israel. Proceedings (Cat. No. 00EX377) (pp. 253–256). IEEE (2000).

  28. Shah, S.M.: Applications of Fractional Derivatives in Adaptive Signal Processing Systems, PhD dissertation, CUST, Islamabad, Pakistan (2019).

  29. Aslam, M.S., Chaudhary, N.I., Raja, M.A.Z.: A sliding-window approximation-based fractional adaptive strategy for Hammerstein nonlinear ARMAX systems. Nonlinear Dyn. 87(1), 519–533 (2017)

    Article  MATH  Google Scholar 

  30. Raja, M.A.Z., Akhtar, R., Chaudhary, N.I., Zhiyu, Z., Khan, Q., Rehman, A.U., Zaman, F.: A new computing paradigm for the optimization of parameters in adaptive beamforming using fractional processing. Eur. Phys. J. Plus 134(6), 275 (2019)

    Article  Google Scholar 

  31. Ye, H.S., Zhou, N.R., Gong, L.H.: Multi-image compression-encryption scheme based on quaternion discrete fractional Hartley transform and improved pixel adaptive diffusion. Signal Process. 175, 107652 (2020).

  32. Hammar, K., Djamah, T., Bettayeb, M.: Identification of fractional Hammerstein system with application to a heating process. Nonlinear Dyn. 96(4), 2613–2626 (2019)

    Article  MATH  Google Scholar 

  33. Mohamed, A.O.U.N., Malti, R., Olivier, C.O.I.S., Oustaloup, A.: System identification using fractional Hammerstein models. IFAC Proc. Vol. 35(1), 265–269 (2002)

    Article  Google Scholar 

  34. Hammar, K., Djamah, T., Bettayeb, M.: Nonlinear system identification using fractional Hammerstein-Wiener models. Nonlinear Dyn. 98(3), 2327–2338 (2019)

    Article  MATH  Google Scholar 

  35. Liao, Z., Zhu, Z., Liang, S., Peng, C., Wang, Y.: Subspace identification for fractional order Hammerstein systems based on instrumental variables. Int. J. Control Autom. Syst. 10(5), 947–953 (2012)

    Article  Google Scholar 

  36. Hammar, K., Djamah, T., Bettayeb, M.: Fractional hammerstein system identification using particle swarm optimization. In: 2015 7th International Conference on Modelling, Identification and Control (ICMIC), pp. 1–6. IEEE (2015).

  37. Cheng, S., Wei, Y., Sheng, D., Wang, Y.: Identification for Hammerstein nonlinear systems based on universal spline fractional order LMS algorithm. Commun. Nonlinear Sci. Numer. Simul. 79, 104901 (2019).

  38. Rahmani, M.R., Farrokhi, M.: Nonlinear dynamic system identification using neuro-fractional-order Hammerstein model. Trans. Inst. Meas. Control. 40(13), 3872–3883 (2018)

    Article  Google Scholar 

  39. Rahmani, M.R., Farrokhi, M.: Fractional-order hammerstein state-space modeling of nonlinear dynamic systems from input–output measurements. ISA Trans. 96, 177–184 (2020)

    Article  Google Scholar 

  40. Hidalgo, D., Cervantes, L., Castillo, O., Melin, P., Martínez Soto, R.: Fuzzy parameter adaptation in genetic algorithms for the optimization of fuzzy integrators in modular neural networks for multimodal biometry. Computación y Sistemas 24(3), 1093–1105 (2020)

    Google Scholar 

  41. Sabir, Z., Raja, M.A.Z., Guirao, J.L., Saeed, T.: Meyer wavelet neural networks to solve a novel design of fractional order pantograph Lane-Emden differential model. Chaos Solitons Fractals 152, 111404 (2021).

  42. Kalia, H., Dehuri, S., Ghosh, A., Cho, S.B.: Surrogate-assisted multi-objective genetic algorithms for fuzzy rule-based classification. Int. J. Fuzzy Syst. 20(6), 1938–1955 (2018)

    Article  Google Scholar 

  43. Sabir, Z., Nisar, K., Raja, M.A.Z., Ibrahim, A.A.B.A., Rodrigues, J.J., Al-Basyouni, K.S., Mahmoud, S.R., Rawat, D.B.: Design of Morlet wavelet neural network for solving the higher order singular nonlinear differential equations. Alex. Eng. J. 60(6), 5935–5947 (2021)

    Article  Google Scholar 

  44. Chhabra, S., Singh, H.: Optimizing design parameters of fuzzy model based cocomo using genetic algorithms. Int. J. Inf. Technol. 12(4), 1259–1269 (2020)

    Google Scholar 

  45. Sabir, Z., Raja, M.A.Z., Wahab, H.A., Altamirano, G.C., Zhang, Y.D., Le, D.N.: Integrated intelligence of neuro-evolution with sequential quadratic programming for second-order Lane-Emden pantograph models. Math. Comput. Simul. 188, 87–101 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  46. Alameer, Z., Abd Elaziz, M., Ewees, A.A., Ye, H., Jianhua, Z.: Forecasting copper prices using hybrid adaptive neuro-fuzzy inference system and genetic algorithms. Nat. Resour. Res. 28(4), 1385–1401 (2019)

    Article  Google Scholar 

  47. Bansal, J.C., Singh, P.K., Pal, N.R. (eds.): Evolutionary and swarm intelligence algorithms, pp. 1–9. Springer, Berlin (2019)

    Google Scholar 

  48. Sabir, Z., Umar, M., Raja, M.A.Z., Baleanu, D.: Applications of Gudermannian neural network for solving the SITR fractal system. Fractals 29(8), p.2150250 (2021).

  49. Xidias, E., Moulianitis, V., Azariadis, P.: Optimal robot task scheduling based on adaptive neuro-fuzzy system and genetic algorithms. Int. J. Adv. Manuf. Technol. 115(3), 927–939 (2021)

    Article  Google Scholar 

  50. Sabir, Z., Raja, M.A.Z., Khalique, C.M., Unlu, C.: Neuro-evolution computing for nonlinear multi-singular system of third order Emden-Fowler equation. Math. Comput. Simul. 185, 799–812 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  51. Pelusi, D., Mascella, R., Tallini, L.: Revised gravitational search algorithms based on evolutionary-fuzzy systems. Algorithms 10(2), 44 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  52. Nisar, K., Sabir, Z., Raja, M.A.Z., Ibrahim, A.A.A., Erdogan, F., Haque, M.R., Rodrigues, J.J., Rawat, D.B.: Design of Morlet wavelet neural network for solving a class of singular pantograph nonlinear differential models. IEEE Access 9, 77845–77862 (2021)

    Article  Google Scholar 

  53. Fedin, A.P., Kalinin, Y.V., Marchuk, E.A.: Antilock braking system fuzzy controller optimization with a genetic algorithm in a form of cellular automaton. In: 2020 4th Scientific School on Dynamics of Complex Networks and their Application in Intellectual Robotics (DCNAIR), pp. 78–81. IEEE (2020).

  54. Sabir, Z., Umar, M., Guirao, J.L., Shoaib, M., Raja, M.A.Z.: Integrated intelligent computing paradigm for nonlinear multi-singular third-order Emden-Fowler equation. Neural Comput. Appl. 33(8), 3417–3436 (2021)

    Article  Google Scholar 

  55. Jamwal, P.K., Abdikenov, B., Hussain, S.: Evolutionary optimization using equitable fuzzy sorting genetic algorithm (EFSGA). IEEE Access 7, 8111–8126 (2019)

    Article  Google Scholar 

  56. Jadoon, I., Raja, M.A.Z., Junaid, M., Ahmed, A., ur Rehman, A. and Shoaib, M.,: Design of evolutionary optimized finite difference based numerical computing for dust density model of nonlinear Van-der Pol Mathieu’s oscillatory systems. Math. Comput. Simul. 181, 444–470 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  57. Ahmed, N., Wang, H., Raja, M.A.Z., Ali, W., Zaman, F., Khan, W.U., He, Y.: Performance analysis of efficient computing techniques for direction of arrival estimation of underwater multi targets. IEEE Access 9, 33284–33298 (2021)

    Article  Google Scholar 

  58. Nisar, K., Sabir, Z., Zahoor Raja, M.A., Ibrahim, A., Asri, A., Rodrigues, J.P.C., J., Shahid Khan, A., Gupta, M., Kamal, A. and Rawat, D.B.: Evolutionary integrated heuristic with Gudermannian neural networks for second kind of Lane-Emden nonlinear singular models. Appl. Sci. 11(11), 4725 (2021)

    Article  Google Scholar 

  59. Sabir, Z., Raja, M.A.Z., Wahab, H.A., Shoaib, M., Aguilar, J.G.: Integrated neuro‐evolution heuristic with sequential quadratic programming for second‐order prediction differential models. Numer. Methods Partial Differ. Equ. (2020).

  60. Sabir, Z., Raja, M.A.Z., Shoaib, M., Aguilar, J.G.: FMNEICS: fractional Meyer neuro-evolution-based intelligent computing solver for doubly singular multi-fractional order Lane-Emden system. Comput. Appl. Math. 39(4), 1–18 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  61. Jadoon, I., Ahmed, A., ur Rehman, A., Shoaib, M. and Raja, M.A.Z.: Integrated meta-heuristics finite difference method for the dynamics of nonlinear unipolar electrohydrodynamic pump flow model. Appl. Soft Comput. 97, 106791 (2020).

  62. Jamal, R., Men, B., Khan, N.H., Raja, M.A.Z.: Hybrid bio-inspired computational heuristic paradigm for integrated load dispatch problems involving stochastic wind. Energies 12(13), 2568 (2019)

    Article  Google Scholar 

  63. Raja, M.A.Z., Aslam, M.S., Chaudhary, N.I., Khan, W.U.: Bio-inspired heuristics hybrid with interior-point method for active noise control systems without identification of secondary path. Front. Inf. Technol. Electron. Eng. 19(2), 246–259 (2018)

    Article  Google Scholar 

  64. Mehmood, A., Zameer, A., Ling, S.H., ur Rehman, A., & Raja, M. A. Z.: Integrated computational intelligent paradigm for nonlinear electric circuit models using neural networks, genetic algorithms and sequential quadratic programming. Neural Comput. Appl. 32(14), 10337–10357 (2020)

    Article  Google Scholar 

  65. Akbar, S., Raja, M.A.Z., Zaman, F., Mehmood, T., Khan, M.A.R.: Design of bio-inspired heuristic techniques hybridized with sequential quadratic programming for joint parameters estimation of electromagnetic plane waves. Wirel. Pers. Commun. 96(1), 1475–1494 (2017)

    Article  Google Scholar 

  66. Raja, M.A.Z., Shah, A.A., Mehmood, A., Chaudhary, N.I., Aslam, M.S.: Bio-inspired computational heuristics for parameter estimation of nonlinear Hammerstein controlled autoregressive system. Neural Comput. Appl. 29(12), 1455–1474 (2018)

    Article  Google Scholar 

  67. Umar, M., Raja, M.A.Z., Sabir, Z., Alwabli, A.S., Shoaib, M.: A stochastic computational intelligent solver for numerical treatment of mosquito dispersal model in a heterogeneous environment. The European Physical Journal Plus 135(7), 1–23 (2020)

    Article  Google Scholar 

  68. Ahmad, I., Ilyas, H., Urooj, A., Aslam, M.S., Shoaib, M., Raja, M.A.Z.: Novel applications of intelligent computing paradigms for the analysis of nonlinear reactive transport model of the fluid in soft tissues and microvessels. Neural Comput. Appl. 31(12), 9041–9059 (2019)

    Article  Google Scholar 

  69. Raja, M.A.Z., Mehmood, A., Khan, A.A., Zameer, A.: Integrated intelligent computing for heat transfer and thermal radiation-based two-phase MHD nanofluid flow model. Neural Comput. Appl. 32(7), 2845–2877 (2020)

    Article  Google Scholar 

  70. Mehmood, A., Afsar, K., Zameer, A., Awan, S.E., Raja, M.A.Z.: Integrated intelligent computing paradigm for the dynamics of micropolar fluid flow with heat transfer in a permeable walled channel. Appl. Soft Comput. 79, 139–162 (2019)

    Article  Google Scholar 

  71. Raja, M.A.Z., Samar, R., Haroon, T., Shah, S.M.: Unsupervised neural network model optimized with evolutionary computations for solving variants of nonlinear MHD Jeffery-Hamel problem. Appl. Math. Mech. 36(12), 1611–1638 (2015)

    Article  MathSciNet  Google Scholar 

  72. Hammar, K., Djamah, T., Bettayeb, M.: May. Fractional Hammerstein CAR system identification. In: 2017 6th International Conference on Systems and Control (ICSC), pp. 476–480. IEEE (2017).

  73. Zhang, K., Hao, W.N., Yu, X.H., Jin, D.W., Zhang, Z.H.: A multitasking genetic algorithm for mamdani fuzzy system with fully overlapping triangle membership functions. Int. J. Fuzzy Syst. 22(8), 2449–2465 (2020)

    Article  Google Scholar 

  74. Abdelrahim, E.M.: Hierarchical adaptive genetic algorithm based T–S fuzzy controller for non-linear automotive applications. Int. J. Fuzzy Syst. 1–15 (2021).

  75. Zhang, C.: Classification rule mining algorithm combining intuitionistic fuzzy rough sets and genetic algorithm. Int. J. Fuzzy Syst. 22, 1694–1715 (2020)

    Article  Google Scholar 

  76. Wang, N., Xu, H., Li, C., Yin, J.: Hierarchical path planning of unmanned surface vehicles: a fuzzy artificial potential field approach. Int. J. Fuzzy Syst. 1–12 (2020).

  77. Choudhary, A., Nizamuddin, M., Sachan, V.K.: A hybrid fuzzy-genetic algorithm for performance optimization of cyber physical wireless body area networks. Int. J. Fuzzy Syst. 22(2), 548–569 (2020)

    Article  Google Scholar 

  78. Chebouba, B.N., Mellal, M.A., Adjerid, S.: Fuzzy multiobjective system reliability optimization by genetic algorithms and clustering analysis. Qual. Reliab. Eng. Int. 37(4), 1484–1503 (2021)

    Article  Google Scholar 

  79. Goldschmid, J., Gude, V., Corns, S.: SoS explorer application with fuzzy-genetic algorithms to assess an enterprise architecture—a healthcare case study. Procedia Computer Science 185, 55–62 (2021)

    Article  Google Scholar 

  80. Consiglio, A., Casalino, G., Castellano, G., Grillo, G., Perlino, E., Vessio, G., Licciulli, F.: Explaining ovarian cancer gene expression profiles with Fuzzy rules and genetic algorithms. Electronics 2021(10), 375 (2021)

    Article  Google Scholar 

  81. Saravana, S., Arulselvi, D.S.: A Fuzzy-GA based controlling system for wireless sensor networks. In: I3CAC 2021, 7–8 June 2021, Bharath University, Chennai, India (2021)

  82. Milan, S.G., Roozbahani, A., Azar, N.A., Javadi, S.: Development of adaptive neuro fuzzy inference system–Evolutionary algorithms hybrid models (ANFIS-EA) for prediction of optimal groundwater exploitation. J. Hydrol. 598, 126258 (2021).

  83. Zhang, X., Wang, H., Stojanovic, V., Cheng, P., He, S., Luan, X., Liu, F.: Asynchronous fault detection for interval type-2 fuzzy nonhomogeneous higher-level markov jump systems with uncertain transition probabilities. IEEE Trans. Fuzzy Syst. (2021)

  84. Xin, X., Tu, Y., Stojanovic, V., Wang, H., Shi, K., He, S., Pan, T.: Online reinforcement learning multiplayer non-zero sum games of continuous-time Markov jump linear systems. Appl. Math. Comput. 412, 126537 (2022).

  85. Cheng, P., Wang, H., Stojanovic, V., He, S., Shi, K., Luan, X. et al.: Asynchronous fault detection observer for 2-D Markov jump systems. IEEE Trans. Cybern. (2021)

  86. Cheng, P., He, S., Stojanovic, V., Luan, X., Liu, F.: Fuzzy fault detection for Markov jump systems with partly accessible hidden information: an event-triggered approach. IEEE Trans. Cybern. (2021).

  87. Wang, B.C., Li, H.X., Feng, Y., Shen, W.J.: An adaptive fuzzy penalty method for constrained evolutionary optimization. Inf. Sci. 571, 358–374 (2021)

    Article  MathSciNet  Google Scholar 

  88. Chuanxin, Y., Xuefeng, Y.A.N.: A fuzzy-based adaptive genetic algorithm and its case study in chemical engineering. Chin. J. Chem. Eng. 19(2), 299–307 (2011)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Graduate School of Engineering Science and Technology, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, 64002, Yunlin, Taiwan, ROC

    Muhammad Faizan Malik

  2. Department of Computer Science and Information Engineering, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, 64002, Yunlin, Taiwan, ROC

    Ching-Lung Chang

  3. School of Electrical, Electronics and Computer Sciences, Guangxi University of Science and Technology, Liuzhou, China

    Muhammad Shamrooz Aslam

  4. Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, 64002, Yunlin, Taiwan, ROC

    Naveed Ishtiaq Chaudhary & Muhammad Asif Zahoor Raja

  5. Department of Electrical and Computer Engineering, COMSATS University Islamabad, Attock Campus, Attock, 43600, Pakistan

    Muhammad Asif Zahoor Raja

Authors
  1. Muhammad Faizan Malik
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ching-Lung Chang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Muhammad Shamrooz Aslam
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Naveed Ishtiaq Chaudhary
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Muhammad Asif Zahoor Raja
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Muhammad Asif Zahoor Raja.

Ethics declarations

Conflict of interest

All the authors of the manuscript declared that there is no any conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Malik, M.F., Chang, CL., Aslam, M.S. et al. Fuzzy-Evolution Computing Paradigm for Fractional Hammerstein Control Autoregressive Systems. Int. J. Fuzzy Syst. 24, 2447–2475 (2022). https://doi.org/10.1007/s40815-022-01291-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-022-01291-2

Keywords

Search

Navigation