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Fractional order controllers increase the robustness of closed-loop deep brain stimulation systems

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  • Coronel-Escamilla, Antonio
  • Gomez-Aguilar, Jose Francisco
  • Stamova, Ivanka
  • Santamaria, Fidel

Abstract

We studied the effects of using fractional order proportional, integral, and derivative (PID) controllers in a closed-loop mathematical model of deep brain stimulation. The objective of the controller was to dampen oscillations from a neural network model of Parkinson's disease. We varied intrinsic parameters, such as the gain of the controller, and extrinsic variables, such as the excitability of the network. We found that in most cases, fractional order components increased the robustness of the model multi-fold to changes in the gains of the controller. Similarly, the controller could be set to a fixed set of gains and remain stable to a much larger range, than for the classical PID case, of changes in synaptic weights that otherwise would cause oscillatory activity. The increase in robustness is a consequence of the properties of fractional order derivatives that provide an intrinsic memory trace of past activity, which works as a negative feedback system. Fractional order PID controllers could provide a platform to develop stand-alone closed-loop deep brain stimulation systems.

Suggested Citation

  • Coronel-Escamilla, Antonio & Gomez-Aguilar, Jose Francisco & Stamova, Ivanka & Santamaria, Fidel, 2020. "Fractional order controllers increase the robustness of closed-loop deep brain stimulation systems," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    • Handle: RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920305452
    DOI: 10.1016/j.chaos.2020.110149
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    References listed on IDEAS

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    1. A. Coronel-Escamilla & J. F. Gómez-Aguilar & E. Alvarado-Méndez & G. V. Guerrero-Ramírez & R. F. Escobar-Jiménez, 2016. "Fractional dynamics of charged particles in magnetic fields," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 27(08), pages 1-15, August.
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    4. Changpin Li & Deliang Qian & YangQuan Chen, 2011. "On Riemann-Liouville and Caputo Derivatives," Discrete Dynamics in Nature and Society, Hindawi, vol. 2011, pages 1-15, March.
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