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Pré-Publication, Document De Travail Année : 2024

Prescribed exponential stabilization of a one-layer neural network with delayed feedback: Insights in seizure prevention and neural control

Résumé

This paper provides control-oriented delay-based modelling of a one-layer neural network of Hopfield-type subject to an external input designed as delayed feedback. The specificity of such a model is that it makes the considered neuron less susceptible to seizure caused by its inherent dynamic instability. This modelling exploits a recently set partial pole placement for linear functional differential equations, which relies on the coexistence of real spectral values, allowing the explicit prescription of the closed-loop solution's exponential decay. The proposed framework improves some pioneering and scarce results from the literature on the characterization of the exact solution's exponential decay when a simple real spectral value exists. Indeed, it improves neural stability when the inherent dynamic is stable and provides insights into the design of a one-layer neural network that can be stabilized exponentially with delayed feedback and with a prescribed decay rate regardless of whether the inherent neuron dynamic is stable or unstable.
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Dates et versions

hal-04617948 , version 1 (19-06-2024)
hal-04617948 , version 2 (21-06-2024)

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  • HAL Id : hal-04617948 , version 1

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Cyprien Tamekue, Islam Boussaada, Karim Liviu Trabelsi. Prescribed exponential stabilization of a one-layer neural network with delayed feedback: Insights in seizure prevention and neural control. 2024. ⟨hal-04617948v1⟩

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