# Intelligent Control of Seizure-Like Activity in a Memristive Neuromorphic Circuit Based on the Hodgkin–Huxley Model

^{1}

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## Abstract

**:**

## 1. Introduction

_{2}and TiO

_{2−x}) films [13,14]. Memristive (or resistive switching) neuromorphic devices present a stimulus response comparable to the synaptic strengthening/weakening process, being intrinsically capable of emulating important brain learning mechanisms, such as short- and long-term plasticity [10,11,15].

## 2. Memristive Neuromorphic Circuit

## 3. Intelligent Control

## 4. Numerical Results

- The intelligent control scheme can adequately handle the unknown external electric current ${I}_{ext}$ and the uncertainties associated with the unmodeled internal states of the memristors, which in fact may allow other different memristive circuits to be controlled by means of the same control framework;
- Online learning, rather than offline training, is adopted to allow the controller to continuously improve its overall performance, even when subjected to dynamically changing circumstances;
- The neural network can learn to compensate for uncertainties and disturbances by minimizing the control error, making direct measurements of the signal to be estimated (which is not possible in real applications) completely unnecessary;
- By combining the artificial neural network with a nonlinear control method, the computational demands on the ANN are minimized, which allows its implementation on low-power embedded hardware and the adoption of the online learning scheme.

## 5. Concluding Remarks

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**(

**a**) Schematic representation of the memristive circuit that describes the action potentials in the axon membrane. Pinched hysteresis loops for the memristors related to (

**b**) sodium- and (

**c**) potassium-gated channels with a voltage of $50\mathrm{sin}\omega t$ mV, three different frequency values and model parameters adopted according to Table 1.

**Figure 6.**Control performance of the conventional scheme: (

**a**) seizure-like activity still present despite of the (

**b**) control signal with higher amplitude when compared with the intelligent scheme.

**Figure 7.**Control performance of the intelligent scheme: (

**a**) seizure-like activity successfully suppressed and (

**b**) control signal with lower amplitude when compared with the conventional scheme.

**Figure 9.**Control performance of the intelligent scheme: (

**a**) seizure-like activity successfully suppressed, even for different setpoints, and (

**b**) corresponding control signal.

${\mathit{C}}_{\mathit{m}}$ | ${\mathit{E}}_{\mathit{Na}}$ | ${\mathit{E}}_{\mathit{K}}$ | ${\mathit{E}}_{\mathit{L}}$ | ${\mathit{g}}_{\mathit{Na}}$ | ${\mathit{g}}_{\mathit{K}}$ | ${\mathit{G}}_{\mathit{L}}$ |
---|---|---|---|---|---|---|

1 µF | 115 mV | 12 mV | $10.599$ mV | 120 mS | 36 mS | $0.3$ mS |

${\mathit{\psi}}_{1}$ | ${\mathit{\psi}}_{2}$ | ${\mathit{\psi}}_{3}$ | ${\mathit{\psi}}_{4}$ | ${\mathit{\psi}}_{5}$ | ${\mathit{\psi}}_{6}$ | |
---|---|---|---|---|---|---|

Centers | $-10.00$ | $-2.50$ | $-1.25$ | $1.25$ | $2.50$ | $10.00$ |

Widths | $10.00$ | $6.67$ | $3.33$ | $3.33$ | $6.67$ | $10.00$ |

**Table 3.**Integral Absolute Error (IAE) and the Integral Absolute Control Input (IACI) for both conventional and intelligent controllers with corresponding achieved percentage reductions.

Conventional | Intelligent | Percentage Reduction | |
---|---|---|---|

IAE [mV s] | $1151.00$ | $4.67$ | $99.59\%$ |

IACI [$\mu $C] | $6907.27$ | $4330.15$ | $37.31\%$ |

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Bessa, W.M.; Lima, G.d.S.
Intelligent Control of Seizure-Like Activity in a Memristive Neuromorphic Circuit Based on the Hodgkin–Huxley Model. *J. Low Power Electron. Appl.* **2022**, *12*, 54.
https://doi.org/10.3390/jlpea12040054

**AMA Style**

Bessa WM, Lima GdS.
Intelligent Control of Seizure-Like Activity in a Memristive Neuromorphic Circuit Based on the Hodgkin–Huxley Model. *Journal of Low Power Electronics and Applications*. 2022; 12(4):54.
https://doi.org/10.3390/jlpea12040054

**Chicago/Turabian Style**

Bessa, Wallace Moreira, and Gabriel da Silva Lima.
2022. "Intelligent Control of Seizure-Like Activity in a Memristive Neuromorphic Circuit Based on the Hodgkin–Huxley Model" *Journal of Low Power Electronics and Applications* 12, no. 4: 54.
https://doi.org/10.3390/jlpea12040054