An adaptive observer is proposed to estimate the synaptic distribution between neurons asymptotically from the measurement of a part of the neuronal activity and a delayed neural field evolution model. The convergence of the observer is proved under a persistency of excitation condition. Then, the observer is used to derive a feedback law ensuring asymptotic stabilization of the neural fields. Finally, the feedback law is modified to ensure simultaneously practical stabilization of the neural fields and asymptotic convergence of the observer under additional restrictions on the system. Numerical simulations confirm the relevance of the approach.

中文翻译：

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时空延迟神经场的自适应观测器和控制

提出了一种自适应观察器，通过对部分神经元活动的测量和延迟神经场演化模型来渐近地估计神经元之间的突触分布。在持续激励条件下证明了观测器的收敛性。然后，使用观察者导出确保神经场渐近稳定的反馈定律。最后，修改反馈定律以确保神经场的实际稳定和观察者在系统附加限制下的渐近收敛。数值模拟证实了该方法的相关性。