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Robust optimal control of nonlinear fractional systems

Author

Listed:
  • Liu, Chongyang
  • Zhou, Tuo
  • Gong, Zhaohua
  • Yi, Xiaopeng
  • Teo, Kok Lay
  • Wang, Song

Abstract

Parameter uncertainty is inevitably found in almost every system and, if is ignored, it could jeopardize the effectiveness of control method. Motivated by this issue, we consider a robust optimal control problem governed by a nonlinear fractional system with uncertain parameters, where the system sensitivity with respect to the uncertain parameters is explicitly included in the cost functional. For this problem, we first prove that the system sensitivity can be expressed as the solution of an auxiliary fractional system. Then, we propose a numerical scheme for discretizing both the original and auxiliary fractional systems, resulting in a finite-dimensional optimization problem. Furthermore, a numerical solution algorithm based on gradients of the cost functional is developed for the resulting optimization problem. Finally, numerical results for two example problems are given to demonstrate the validity and applicability of the proposed algorithm.

Suggested Citation

  • Liu, Chongyang & Zhou, Tuo & Gong, Zhaohua & Yi, Xiaopeng & Teo, Kok Lay & Wang, Song, 2023. "Robust optimal control of nonlinear fractional systems," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    • Handle: RePEc:eee:chsofr:v:175:y:2023:i:p1:s0960077923008652
    DOI: 10.1016/j.chaos.2023.113964
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    References listed on IDEAS

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    1. Chongyang Liu & Zhaohua Gong & Changjun Yu & Song Wang & Kok Lay Teo, 2021. "Optimal Control Computation for Nonlinear Fractional Time-Delay Systems with State Inequality Constraints," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 83-117, October.
    2. Shu-Bo Chen & Samaneh Soradi-Zeid & Maryam Alipour & Yu-Ming Chu & J. F. Gã“Mez-Aguilar & Hadi Jahanshahi, 2021. "Optimal Control Of Nonlinear Time-Delay Fractional Differential Equations With Dickson Polynomials," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(04), pages 1-16, June.
    3. Li, Jun-Feng & Jahanshahi, Hadi & Kacar, Sezgin & Chu, Yu-Ming & Gómez-Aguilar, J.F. & Alotaibi, Naif D. & Alharbi, Khalid H., 2021. "On the variable-order fractional memristor oscillator: Data security applications and synchronization using a type-2 fuzzy disturbance observer-based robust control," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    4. Chongyang Liu & Changjun Yu & Zhaohua Gong & Huey Tyng Cheong & Kok Lay Teo, 2023. "Numerical Computation of Optimal Control Problems with Atangana–Baleanu Fractional Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 798-816, May.
    5. Chongyang Liu & Zhaohua Gong & Kok Lay Teo & Song Wang, 2022. "Optimal Control of Nonlinear Fractional-Order Systems with Multiple Time-Varying Delays," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 856-876, June.
    6. Bo Wang & Hadi Jahanshahi & Stelios Bekiros & Yu-Ming Chu & J. F. Gã“Mez-Aguilar & Fawaz E. Alsaadi & Madini O. Alassafi, 2021. "Tracking Control And Stabilization Of A Fractional Financial Risk System Using Novel Active Finite-Time Fault-Tolerant Controls," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(06), pages 1-20, September.
    7. Wang, Yong-Long & Jahanshahi, Hadi & Bekiros, Stelios & Bezzina, Frank & Chu, Yu-Ming & Aly, Ayman A., 2021. "Deep recurrent neural networks with finite-time terminal sliding mode control for a chaotic fractional-order financial system with market confidence," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    8. Kok Lay Teo & Bin Li & Changjun Yu & Volker Rehbock, 2021. "Applied and Computational Optimal Control," Springer Optimization and Its Applications, Springer, number 978-3-030-69913-0, July.
    9. Xiong, Pei-Ying & Jahanshahi, Hadi & Alcaraz, Raúl & Chu, Yu-Ming & Gómez-Aguilar, J.F. & Alsaadi, Fawaz E., 2021. "Spectral Entropy Analysis and Synchronization of a Multi-Stable Fractional-Order Chaotic System using a Novel Neural Network-Based Chattering-Free Sliding Mode Technique," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
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    Cited by:

    1. Wang, Yue & Wei, Wei, 2024. "Optimal control problem governed by a kind of Kirchhoff-type equation," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).

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