【作者】 刘丹；

【导师】 罗小元；

【作者基本信息】 燕山大学 ， 控制科学与工程， 2020， 博士

【摘要】 经颅磁声刺激是一种兼具高空间分辨率和高穿透深度的新型脑刺激技术。目前,经颅磁声刺激的研究处于理论分析与动物实验阶段,但仍需要大量的基础研究作为临床应用的依据。通过具有磁声刺激输入的神经元模型,可模拟经颅磁声刺激作用下真实神经元的放电行为。针对磁声刺激输入下神经元模型放电特性与同步控制的研究,有助于进一步揭示经颅磁声刺激的作用机制,加深对磁声刺激作用下神经系统放电特性的理解。为此,本文基于磁声刺激输入下神经元模型进行了放电特性分析与同步控制研究,主要研究内容如下:1)针对磁声刺激输入下Ermentrout神经元模型的脉冲频率适应特性问题,研究了不同磁声参数对神经元脉冲频率适应特性的影响。首先,通过仿真实验绘制了不同磁声参数下神经元的膜电位时间响应曲线和脉冲频率时间响应曲线,分析了磁声参数对神经元适应过程的影响。其次,通过不同磁声参数下神经元的初始脉冲频率适应特性曲线,进一步研究了磁声参数对神经元脉冲频率适应特性的影响,并对主要结论的生理机制进行了研究分析。2)针对磁声刺激输入下分数阶扩展HR神经元模型的动态特性问题,研究了不同磁声参数对神经元稳定状态下的放电模式和放电节律的影响。首先,基于更符合神经元复杂放电特性的分数阶扩展HR神经元模型,通过仿真实验绘制了不同磁声参数下神经元的膜电位曲线以及峰峰间隔分岔图,定量分析了不同磁声参数对应的神经元放电模式和放电节律。其次,通过对比分数阶与整数阶神经元的膜电位峰峰间隔分岔图,进一步研究了分数阶神经元模型的复杂动态特性。3)针对磁声刺激输入下分数阶扩展HR神经元模型的同步问题,设计了自适应神经网络滑模控制器,实现了主从神经元模型系统的同步控制。首先,基于分数阶定义和性质,引入了新的滑模面,并由此构造主从神经元同步误差系统。其次,在考虑神经元模型具有未知非线性参数和未知外部扰动的前提下,提出了自适应神经网络滑模控制策略,控制从神经元克服不确定参数和外部扰动的影响,达到与主神经元相同的状态轨迹。4)针对磁声刺激输入下分数阶扩展HR神经元模型的广义投影同步问题,设计了自适应模糊控制器,实现了主从神经元系统的广义投影同步。首先,针对具有不同分数阶次的主从神经元模型系统,基于分数阶性质引入新的同步误差变量,并构造了广义投影同步误差系统。其次,在考虑神经元系统具有全部未知参数和未知扰动的情况下,设计了自适应模糊广义投影同步控制算法,通过选取合适的控制参数,可实现主从神经元系统状态轨迹的完全同步、反相同步和投影同步。5)针对磁声刺激输入下HH神经元模型的预定性能同步问题,设计了自适应神经网络控制器,实现了主从连接神经元膜电位的预定性能同步。首先,考虑主从神经元模型具有不同的模型参数,通过状态转换方程设计滤波器误差,构造了无约束的滤波同步误差系统。其次,在考虑神经元模型具有不确定参数和非线性特性基础上,设计了稳定的自适应神经网络同步控制器,实现了主从神经元膜电位同步,且保证其同步性能满足预设约束条件。更多还原

【Abstract】 Transcranial magneto-acoustical stimulation(TMAS)is considered as a potentially effective treatment for neurological disorders as its advantages in terms of spatial resolution and penetration depth.Nowadays,the research on TMAS is mainly carried out through theoretical analysis and animal experiment,and still require a large amount of basic work as the guideline for clinical application.The neuronal model with magneto-acoustical stimulation input can simulate the electrical activities of neurons stimulated by TMAS.The research on the firing properties and synchronization control of the neuronal model with magneto-acoustical stimulation input contributes to the understanding of the mechanism of TMAS and the discharge characteristics of the nervous system under magneto-acoustical stimulation.Given this,this thesis investigates the firing characteristic and synchronization control of the neuronal models with magneto-acoustical stimulation input,and the main research contents are given as follows:(1)For the spike-frequency adaptation characteristics of the Ermentrout neuronal model with magneto-acoustical input,the effects of the different magnetic field and ultrasonic parameters on neural spike-frequency adaptation are analyzed.Firstly,based on the simulation experiment,the membrane potential curves and spike-frequency curves under different magnetic field and ultrasonic parameters are generated,and the effect of these parameters on the adaptation process of the neuron are analyzed.Moreover,the adapted onset spike-frequency curves with different input parameters and initial values of the adaptive variable are exhibited to investigate the effect of the different magnetic field and ultrasonic parameters on the neural spike-frequency adaptation.Finally,the physiological mechanism of the conclusions is discussed.(2)For the firing characteristic of the fractional-order extended Hindmarsh-Rose(HR)neuronal model with magneto-acoustical stimulation input,the effect of the different magnetic field and ultrasonic parameters on the firing mode and firing rhythm of the neuronal model are investigated.Firstly,the fractional-order extended HR neuronal model which has been verified to be more consistent with the biological characteristics of a neuron is considered.Based on the simulation experiment,the membrane potential curves under different magnetic field and ultrasonic parameters,and the corresponding interspike interval diagrams are generated and analyzed,then the firing modes and firing rhythms of the neuronal model with the different magnetic field and ultrasonic parameters are concluded.In addition,the complex dynamic properties of the fractional-order neuronal model are explored by comparing the interspike interval diagrams of the membrane potential curves of the fractional-order neuronal model to those of the integer-order neuronal model.(3)For the synchronization for the fractional-order extended HR neuronal model with magneto-acoustical stimulation input,an adaptive neural network controller is designed to achieve the synchronization control of the master-slave system of neuronal models.Based on the fractional-order definition and properties,a new sliding surface is introduced to construct the synchronization error system of the master and slave neuronal models.Considering the nonlinearity and uncertain parameters of the neuronal model as well as the unknown external disturbances,an adaptive neural network slide mode control scheme is proposed to make the slave neuron realize resilience for the uncertain parameters and the external disturbances,and achieve synchronous rhythms of the membrane potentials with those of the master neuron.(4)For the generalized projective synchronization for the fractional-order extended HR neuronal model with magneto-acoustical stimulation input,an adaptive fuzzy controller is designed to achieve the generalized projective synchronization control of the master-slave system of neuronal models.Based on the master and slave neuronal model with different fractional orders,new synchronization errors are introduced to construct the generalized projective synchronization error system.Considering the uncertain parameters of the neuronal model and the unknown external disturbances,an adaptive fuzzy generalized projective synchronization control algorithm is designed.By choosing the appropriate design parameters,the proposed control scheme enables the master-slave neuron system to achieve complete synchronization,anti-phase synchronization,and generalized projective synchronization in a finite amount of time and to be resilient to uncertain parameters and unknown disturbances.(5)For the prescribed performance synchronization of the Hodgkin-Huxley(HH)neuronal model with magneto-acoustical stimulation input,an adaptive neural network controller is designed to achieve the prescribed performance synchronization of the masterslave system of the HH neuronal models.By taking the different model parameters of the master and slave neurons into consideration,a new filter error is introduced by state transformation to make the equivalent unconstrained stabilization control problem instead of the constrained tracking problem.A stable adaptive neural network synchronization controller is designed to overcome the nonlinearity and uncertainties of the neuronal model and ensure the synchronization status of the master and slave neurons,as well as the prescribed synchronization performance in the processes of synchronization.更多还原