Department of Electrical and Systems Engineering, Washington University, Saint Louis, MO 63130, USA.
J Neural Eng. 2012 Aug;9(4):046015. doi: 10.1088/1741-2560/9/4/046015. Epub 2012 Jul 12.
In this paper, we derive the minimum-energy periodic control that entrains an ensemble of structurally similar neural oscillators to a desired frequency. The state-space representation of a nominal oscillator is reduced to a phase model by computing its limit cycle and phase response curve, from which the optimal control is derived by using formal averaging and the calculus of variations. We focus on the case of a 1:1 entrainment ratio and suggest a simple numerical method for approximating the optimal controls. The method is applied to asymptotically control the spiking frequency of neural oscillators modeled using the Hodgkin-Huxley equations. Simulations are used to illustrate the optimality of entrainment controls derived using phase models when applied to the original state-space system, which is crucial for using phase models in control synthesis for practical applications. This work addresses a fundamental problem in the field of neural dynamics and provides a theoretical contribution to the optimal frequency control of uncertain oscillating systems.
在本文中，我们推导出最小能量周期控制，以使一组结构相似的神经振荡器被锁定到期望的频率。通过计算标称振荡器的极限环和相位响应曲线，将其状态空间表示简化为相模型，然后通过使用形式平均和变分法导出最佳控制。我们专注于 1:1 锁定比的情况，并提出了一种简单的数值方法来近似最佳控制。该方法应用于渐近控制使用 Hodgkin-Huxley 方程建模的神经振荡器的尖峰频率。仿真用于说明应用于原始状态空间系统时使用相模型推导的锁定控制的最优性，这对于在控制合成中使用相模型进行实际应用至关重要。这项工作解决了神经动力学领域的一个基本问题，并为不确定振荡系统的最佳频率控制提供了理论贡献。
