Using Synchronization of Dynamical Systems for Verification and Validation of Neurobiological Models: Experiment and Theory

在这个项目中，PI将开发一种使用实验数据来估计神经生物系统模型中的状态和参数的非线性动力学方法。利用这种方法，PI将分析甲壳类幽门中央模式发生器(CPG)中单个神经元的模型以及该CPG内神经元子电路的模型。确定单个神经元的数学模型和神经元网络的参数的一般问题将使用一种称为动态参数估计(DPE)的新方法来解决，该方法基于期望轨迹的最优跟踪的经典问题。在这种情况下，DPE在控制理论文献中被称为具有自适应增益的Luenberger观测器：卡尔曼意义上的滤波器。使用这种方法，PI将应用新技术来分析来自CPG神经元和CPG子电路的实验数据。两名研究生将参与这项工作。PI的研究小组还将在每年夏天与加州大学圣地亚哥分校的本科生研究经验(REU)项目一起工作。

In this project the PI will develop a nonlinear dynamical method for the estimation of states and parameters in models of neurobiological systems using experimental data. Utilizing this method the PI will analyze models of individual neurons in the crustacean Pyloric central pattern generator (CPG) and models of sub-circuits of neurons within this CPG. The general problem of determining the parameters of mathematical models of individual neurons and networks of neurons will be addressed using a novel method called dynamical parameter estimation (DPE), which is based on the classical problem of optimal tracking of a desired trajectory. In this case the DPE is known in the control theory literature as a Luenberger observer with adaptive gain: a filter in the sense of Kalman. Using this approach the PI will apply the new technique to the analysis of experimental data from CPG neurons and CPG sub-circuits. Two graduate students will be involved in this efforts. The research group of the PI will also work each summer with Research Experience for Undergraduates (REU) undergraduate students program at UCSD.