AI 中文总结
本研究针对仅作用于固定子集的受控Amari型神经场，在适当假设下证明其线性化形式开环可镇定，进而推导闭环可镇定性，还通过数值模拟获取控制代价的经验估计。
AI 中文摘要
神经工程中的一个重要问题是神经场的镇定。在实际应用中，通常假设执行器的位置可以任意选择。本研究探讨受控Amari型神经场的可镇定性，其中控制输入仅作用于神经场的固定子集。我们证明，在相互作用强度的适当假设以及控制集的温和相对密度假设下，线性化神经场是开环可镇定的。该几何假设要求每个立方体与控制集的交集体积有下界。由此，我们在传感器/执行器位置约束下推导得出神经场的闭环可镇定性，并通过数值模拟说明结果，获得控制代价的经验估计。
英文摘要
An important problem in neuro-engineering is the stabilization of neural fields. In applications, it is often assumed that the actuator placement can be chosen arbitrarily. In this work, we investigate the stabilizability of controlled Amari-type neural fields where the control input is prescribed to act only on a fixed subset of the neural field. We show that the linearized neural field is open-loop stabilizable under suitable assumptions on the interaction strength and a mild relative density assumption on the control set. Our geometric assumption requires that the volume of each cube intersected with the control set must be bounded below. As a consequence, we derive closed-loop stabilizability of the neural fields, under sensor/actuator placement constraints. Numerical simulations are used to illustrate the results and obtain empirical estimates on the control cost.
CommentsAccepted at IEEE MetroXRAINE
