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A novel fractional-order integral dynamical backstepping controller design for integer-order nonlinear systems: An application to mock cardiovascular circulatory system

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  • Hedayati, Shahrzad
  • Nozari, Hasan Abbasi
  • Rostami, Seyed Jalil Sadati

Abstract

This paper proposes a novel conformable fractional-order integral dynamical backstepping (CFOIDBST) design procedure by incorporating conformable fractional calculus into the classical dynamical backstepping (DBST) approach. The primary objective is to develop a robust control strategy that improves control performance and handles inter- and intra-patient parameter uncertainties in an integer-order cardiovascular circulatory system. The CFOIDBST approach is applied to a system where a piston pump acts as a mock ventricle coupled with high-bandwidth pressure dynamics and nonlinearities due to the check valves. A simulated clinical trial based on the Monte-Carlo (MC) method is proposed to investigate patient-to-patient variability and confirms that the CFOIDBST controller outperforms other control design approaches, attributed to an extra fractional-order tuning parameter. Additionally, the stability of the closed-loop system, represented by integro-differential dynamics, is investigated based on the Lyapunov theorem.

Suggested Citation

  • Hedayati, Shahrzad & Nozari, Hasan Abbasi & Rostami, Seyed Jalil Sadati, 2025. "A novel fractional-order integral dynamical backstepping controller design for integer-order nonlinear systems: An application to mock cardiovascular circulatory system," Chaos, Solitons & Fractals, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:chsofr:v:192:y:2025:i:c:s0960077925000049
    DOI: 10.1016/j.chaos.2025.115991
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    References listed on IDEAS

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    1. Mohsen Bakouri & Ahmed Alassaf & Khaled Alshareef & Saleh Abdelsalam & Husham Farouk Ismail & Ali Ganoun & Abdul-Hakeem Alomari, 2022. "An Optimal H-Infinity Controller for Left Ventricular Assist Devices Based on a Starling-like Controller: A Simulation Study," Mathematics, MDPI, vol. 10(5), pages 1-17, February.
    2. Jeongeun Son & Dongping Du & Yuncheng Du, 2019. "Stochastic Modeling and Dynamic Analysis of the Cardiovascular System with Rotary Left Ventricular Assist Devices," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-18, January.
    3. Mohsen Bakouri & Ahmad Alassaf & Khaled Alshareef & Amor Smida & Ibrahim AlMohimeed & Abdulrahman Alqahtani & Mohamed Abdelkader Aboamer & Yousef Alharbi, 2022. "A Feasible Method to Control Left Ventricular Assist Devices for Heart Failure Patients: A Numerical Study," Mathematics, MDPI, vol. 10(13), pages 1-17, June.
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