124
Views
3
CrossRef citations to date
0
Altmetric
Research Article

Presentation of the model and optimal control of non-linear fractional-order chaotic system of glucose–insulin

ORCID Icon &
Pages 836-848 | Received 30 Nov 2022, Accepted 17 Apr 2023, Published online: 05 May 2023

References

  • Acikgoz SU, Diwekar UM. 2010. Blood glucose regulation with stochastic optimal control for insulin-dependent diabetic patients. Chem Eng Sci. 65(3):1227–1236.
  • Ahmed E, El-Sayed AMA, El-Saka HAA. 2007. Equilibrium points, stability and numerical solutions of fractional order predator-prey and rabies models. J Math Anal Appl. 325(1):542–553.
  • Batmani Y, Khodakaramzadeh S. 2020. Blood glucose concentration control for type 1 diabetic patients: a multiple-model strategy. IET Syst Biol. 14(1):24–30.
  • Batmani Y. 2017. Blood glucose concentration control for type 1 diabetic patients: a non-linear suboptimal approach. IET Syst Biol. 11(4):119–125.
  • Betül Y. 2021. Robust design of electric vehicle components using a new hybrid salp swarm algorithm and radial basis function-based approach. Int J Veh Des. 83(1):38–53.
  • Cho NH, Shaw JE, Karuranga S, Huang Y, da Rocha Fernandes JD, Ohlrogge AW, Malanda B. 2018. IDF diabetes atlas: global estimates of diabetes prevalence for 2017 and projections for 2045. Diabetes Res Clin Pract. 138:271–281.
  • Delshad SS, Asheghan MM, Beheshti MH. 2011. Synchronization of N-coupled incommensurate fractional-order chaotic systems with ring connection. Commun Nonlinear Sci Numer Simul. 16(9):3815–3824.
  • Deng W, Li C, lU J. 2007. Stability analysis of linear fractional differential system with multiple time delays. Nonlinear Dyn. 48(4):409–416.
  • Gupta S, Abderazek H, Yıldız BS, Yildiz AR, Mirjalili S, Sait SM. 2021. Comparison of metaheuristic optimization algorithms for solving constrained mechanical design optimization problems. Expert Syst Appl. 183:115351.
  • Gürses D, Bureerat S, Sait S, Yıldız A. 2021. Comparison of the arithmetic optimization algorithm, the slime mold optimization algorithm, the marine predators algorithm, the salp swarm algorithm for real-world engineering applications. Mater Test. 63(5):448–452.
  • Hegazi AS, Ahmed E, Matouk AE. 2013. On chaos control and synchronization of the commensurate fractional order Liu system. Commun Nonlinear Sci Numer Simul. 18(5):1193–1202.
  • Ibbini M, Masadeh M, Bani Amer M. 2004. A semiclosed-loop optimal control system for blood glucose level in diabetics. J Med Eng Technol. 28(5):189–196.
  • Irma Y, Chávez S, Morales-Menéndez R. 2009. Glucose optimal control system in diabetes treatment. Glucose Optimal Control Syst Diabetes Treat. 209(1):19–30. volume
  • Khan MW, Abid M, Khan AQ, Mustafa G, Ali M, Khan A. 2020. Sliding mode control for a fractional-order non-linear glucose-insulin system. IET Syst Biol. 14(5):223–229.
  • Lee SH, Shin JH, Koo MO, Jung ES, Jeon GI, Park E, Park HR, Lee SC. 2007. Antioxidant and antigenotoxic activities of extracts from anglerfish. J Korean Soc Food Sci Nutr. 36(10):1229–1234.
  • Liu X, Hong L, Yang L, Tang D. 2019. Bifurcations of a new fractional-order system with a one-scroll chaotic attractor. Discrete Dyn Nat Soc. 2019:1–15.
  • Matiognon D. 1996. Stability results for fractional differential equations with applications to control processing. In Computational Engineering in Systems and Application MultiConference, Vol.2, IMACS, IEEE-SMC Proceedings, Lille, France, p. 963–968.
  • Merrikh-Bayat F. 2013. More Details on Analysis of Fractional-Order Lotka-Volterra Equation. In The Fifth IFAC Symposium on Fractional Differentiation and Its Applications (FDA12), 14–17 May 2012, Hohai University, Nanjing, China, p. 1401.0103.
  • Moaddy K, Freihat A, Al-Smadi M, Abuteen E, Hashim I. 2018. Numerical investigation for handling fractional-order Rabinovich–Fabrikant model using the multistep approach. Soft Comput. 22(3):773–782.
  • Narayanan G, Syed Ali M, Rajchakit G, Jirawattanapanit A, Priya B. 2023. Stability analysis for Nabla discrete fractional-order of Glucose–Insulin Regulatory System on diabetes mellitus with Mittag-Leffler kernel. Biomed Signal Process Control. 80(1):104295.
  • Panagant N, Pholdee N, Bureerat S, Kaen K, Yıldız AR, Sait SM. 2020. Seagull optimization algorithm for solving real-world design optimization problems. Mater Test. 62(6):640–644.
  • Parker RS, Doyle FJ, Peppas NA. 2001. The intravenous route to blood glucose control. IEEE Eng Med Biol Mag. 20(1):65–73.
  • Petráš I, Bednárová D. 2009. Fractional - order chaotic systems. In 2009 IEEE Conference on Emerging Technologies & Factory Automation, p. 1–8.
  • Petráš I. 2010. A note on the fractional-order Volta’s system. Commun Nonlinear Sci Numer Simul. 15(2):384–393.
  • Saleh Tavazoei M, Haeri M. 2007. A necessary condition for double scroll attractor existence in fractional-order systems. Phys Lett A. 367(1–2):102–113.
  • Saleh Tavazoei M, Haeri M. 2008. Chaotic attractors in incommensurate fractional order systems. Physica D. 237(20):2628–2637.
  • Shahiri M, Ghaderi R, Ranjbar N A, Hosseinnia SH, Momani S. 2010. Chaotic fractional-order Coullet system: synchronization and control approach. Commun Nonlinear Sci Numer Simul. 15(3):665–674. volume
  • Tavazoei MS, Haeri M, Attari M, Bolouki S, Siami M. 2009. More details on analysis of fractional-order Van der Pol Oscillator. J Vib Control. 15(6):803–819.
  • Tavazoei MS, Tavakoli-Kakhki M, Bizzarri F. 2020. Nonlinear fractional-order circuits and systems: motivation, a brief overview, and some future directions. IEEE Open J Circuits Syst. 1:220–232.
  • Tavazoei MS. 2020. Fractional order chaotic systems: history, achievements, applications, and future challenges. Eur Phys J Spec Top. 229(6–7):887–904.
  • Vakili S, Toosian Shandiz H. 2019. Fractional order glucose insulin system using fractional back-stepping sliding mode control. Int J Nonlinear Anal Appl. 10(2):1–10.
  • Wang Z, Huang X, Shi G. 2011. Analysis of nonlinear dynamics and chaos in a fractional order financial system with time delay. Comput Math Appl. 62(3):1531–1539. volume
  • Yildiz A, Erdaş M. 2021. A new Hybrid Taguchi-salp swarm optimization algorithm for the robust design of real-world engineering problems. Mater Test. 63(2):157–162.
  • Yıldız B, Kumar S, Pholdee N, Bureerat S, Sait S, Yildiz A. 2022. A new chaotic Lévy flight distribution optimization algorithm for solving constrained engineering problems. Expert Syst. 39(8):1–14.
  • Yıldız BS, Patel V, Pholdee N, Sait SM, Bureerat S, Yıldız AR. 2021. Conceptual comparison of the ecogeography-based algorithm, equilibrium algorithm, marine predators algorithm and slime mold algorithm for optimal product design. Mater Test. 63(4):336–340.
  • Yıldız BS, Pholdee N, Bureerat S, Yıldız AR, Sait SM. 2020. Sine-cosine optimization algorithm for the conceptual design of automobile components. Materialpruefung/Mater Test. 62(7):744–748.
  • Yildiz BS, Pholdee N, Bureerat S, Yildiz AR, Sait SM. 2021. Robust design of a robot gripper mechanism using new hybrid grasshopper optimization algorithm. Expert Syst. 38(3):e12666.
  • Yildiz BS, Pholdee N, Bureerat S, Yildiz AR, Sait SM. 2022. Enhanced grasshopper optimization algorithm using elite opposition-based learning for solving real-world engineering problems. Eng Comput. 38(5):4207–4219.
  • Yıldız BS, Pholdee N, Panagant N, Bureerat S, Yildiz AR, Sait SM. 2022. A novel chaotic Henry gas solubility optimization algorithm for solving real-world engineering problems. Eng Comput. 38(S2):871–883.
  • Yildiz. 2020. Slime mould algorithm and kriging surrogate model-based approach for enhanced crashworthiness of electric vehicles. Int J Vehicle Design. 83(1):54–68.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.