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基于脑脉冲序列的离散时间动态系统学习控制研究
韩立元
2024-05-12
Pages144
Subtype博士
Abstract

大脑是一个高度离散且复杂的动态系统,如何将微观的神经脉冲序列与外部世界的宏观信号连接起来,一直是计算神经科学、现代控制理论和人工智能研究领域极为关注的问题。与人工生成的脉冲序列相比,大脑产生的脉冲序列不仅具有生物学的真实性和复杂环境的适应性,还可以并行传输信息,能够精准表征大脑对外部世界多模态信息的感知、处理和控制。因此,基于大脑脉冲序列的离散动态系统的学习控制研究,对于类脑计算与建模、脑机接口开发、神经疾病治疗等多个应用领域具有重要的支撑和指导作用。本文结合了脉冲神经网络的生物合理性、现代控制理论的非线性系统建模能力以及深度学习模拟人脑工作原理的优势,从神经元节点层面、神经网络层面以及实际应用层面,围绕脑脉冲序列的离散时间动态系统学习控制问题进行深入研究。具体地,本文系统地研究了基于泊松过程的脉冲离散时间动态系统自适应学习控制、基于递归最小二乘的离散脉冲网络多尺度动态学习控制以及基于运动皮层跨天脉冲序列的动态对齐学习与解码控制三个问题。本文的主要内容和贡献概括为如下三个方面:
     基于泊松过程的脉冲离散时间动态系统自适应学习控制。针对“传统的脉冲控制问题中没有考虑真实的脉冲序列,只是人为固定脉冲间隔集合”的问题,提出了一种新的生物启发式脉冲自适应动态规划(Spiking Adaptive Dynamic Programming, SADP)方法,用于求解基于脑脉冲序列的离散时间非线性系统的最优脉冲控制问题,有效地改变了传统的脉冲控制方法中人工固定脉冲间隔集合的范式。用泊松过程对脑脉冲进行建模并构建包含状态、脉冲间隔数和概率的三元组,保证了贝尔曼方程只需优化脉冲控制律,而非同时最优化脉冲间隔和脉冲控制律,满足了迭代求解的条件。对SADP方法收敛性的分析,从理论上保证了脉冲值函数可以迭代地收敛到最优性能指标函数。最后,使用Potter实验室开源数据集,在两个数值仿真实例上证明了SADP方法的有效性。
      基于递归最小二乘的离散脉冲网络多尺度动态学习控制。针对“脑内局部离散信号和脑外全局连续信号缺少多尺度协同统一分析理论”的问题,提出了一种离散信息多尺度转换的理论方法,实现了微观的脉冲、介观的脉冲发射率与宏观的行为信号之间的转换。在宏观尺度上,提出并从理论上推导了直接动态规划(Direct Dynamic Programming, DDP)方法,用于模拟固定终端时间和终端状态的最优运动轨迹。在介观尺度上,采用递归最小二乘法(Recursive Least Square, RLS)对脉冲神经网络的突触强度进行实时修正,以适应并处理由离散的微观的脉冲群体发射率表征的介观尺度信号。仿真实验包括了两种运动控制任务和一项脑机接口任务,即点到点控制任务、洛伦兹系统学习任务以及中心外到达且返回任务,每项任务均展现了独特的动力学特征。实验结果证明了所提出的多尺度理论分析方法不仅具有有效性和可解释性,而且可以被应用于实际的脑机接口场景中。
      基于运动皮层跨天脉冲序列的动态对齐学习与解码控制。针对“跨天脉冲序列数据分布不一致导致的解码模型泛化能力不足”的问题,提出了多重对齐的卷积无监督域适应(Multiple Aligned Convolutional Unsupervised Domain Adaption, MACUDA)方法,实现了跨天脉冲数据的稳定性解码。具体来说,MACUDA包括三个过程:降维、多重对齐和解码。该模型先使用具有对比学习损失函数的非线性神经网络将微观的脉冲序列降维,得到介观的高质量神经流形嵌入。MACUDA的多重对齐方法实现了介观的跨天神经流形在统一的稳定流形空间中对齐,接着将对齐后的数据输入到一个基于卷积神经网络的多源域适应解码器中,进而稳定地解码出宏观行为信号。在脑机接口的中心外到达(Center-and-Out Reach, COR)任务的应用场景中,大量的对比实验表明了MACUDA方法在跨天脉冲序列解码任务中有较高的泛化性能,且内部的消融实验证明了MACUDA中多重对齐方法的有效性。

Other Abstract

The brain, as a highly discrete and complex dynamic system, has always been a focal point of research in computational neuroscience, modern control theory, and artificial intelligence, particularly in terms of linking its microscopic neural spike trains to the macro signals of the external world. Compared to artificially generated spike trains, those produced by the brain not only possess biological authenticity and adaptability to complex environments but also exhibit an impressive parallel transmitting capability, representing precisely the brain's perception, processing, and control of multimodal information from the external world. Therefore, studying the learning and control of discrete dynamic systems based on brain spike trains plays a crucial role in supporting and guiding various application domains such as brain-inspired computing and modeling, development of brain-computer interfaces, and treatment of neurological disorders. This thesis integrates the biological plausibility of spiking neural networks, the nonlinear system modeling capabilities of modern control theory, and the advantage of deep learning in simulating the working principles of the human brain to conduct an in-depth investigation into the control problems of discrete-time dynamic systems based on brain spike trains, covering aspects from the level of single neural node and neural networks to applications. Specifically, the thesis systematically explores core topics such as adaptive learning control of spiking discrete-time dynamical systems based on Poisson Process, multiscale dynamic learning control of discrete spiking networks based on recursive least square, and dynamic alignment learning and decoding control based on cross-day spike trains in the motor cortex. The main content and contributions of this thesis can be summarized into the following three aspects: 

    Adaptive learning control of spiking discrete-time dynamical systems based on Poisson Process. Addressing the issue that traditional impulsive control problems do not consider real spike trains but merely use artificially fixed impulsive intervals, a new biologically inspired method called Spiking Adaptive Dynamic Programming (SADP) has been proposed to solve the optimal spiking control problem in discrete-time nonlinear systems based on brain spike trains, effectively changing the paradigm of using fixed impulsive intervals in traditional impulsive control methods. By modeling spike trains with the Poisson process and constructing a 3-tuple consisting of state, number of spiking intervals, and probability, it ensures that the Bellman equation only needs to optimize the spiking control law, rather than optimizing both the spiking intervals and the spiking control law simultaneously, meeting the conditions for iterative solutions. The analysis of the convergence of the SADP method theoretically guarantees that the spiking value function will iteratively converge to the optimal performance index function. Finally, using the open-source dataset from Potter's lab, the effectiveness of the SADP method is demonstrated on two numerical simulation examples.
    Multiscale dynamic learning control of discrete spiking networks based on recursive least square. Addressing the issue of a lack of multiscale collaborative and unified analysis between discrete signals inside the brain and continuous signals outside the brain, this thesis proposes a theoretical method for the transformation of discrete information across different scales. At the macroscopic scale, the Direct Dynamic Programming (DDP) method is theoretically derived for simulating optimal motion trajectories with fixed terminal time and state. At the mesoscopic scale, the Recursive Least Square (RLS) method is employed to adjust the synaptic strengths of spiking neural networks in real-time, adapting to and processing mesoscale signals represented by the population firing rate of discrete microscale spikes. Simulation experiments include two motion control tasks and one brain-computer interface task: a point-to-point control task, learning the Lorenz system task, and a center-out-and-back task, each displaying unique dynamical characteristics. The results demonstrate the effectiveness and interpretability of the proposed multiscale theoretical analysis method, showing its applicability in practical brain-computer interface scenarios.
    Dynamic alignment learning and decoding control based on cross-day spike trains in the motor cortex. To tackle the issue of insufficient generalization capability of decoding models due to inconsistent distribution of cross-day spike trains, a Multiple Aligned Convolutional Unsupervised Domain Adaptation (MACUDA) method is proposed, achieving stable decoding of cross-day spike trains. Specifically, MACUDA involves three processes: dimensionality reduction, multiple alignment, and decoding. The model first reduces the dimensionality of microscopic spike trains through a nonlinear neural network with a contrastive learning loss function, obtaining mesoscale high-quality neural manifold embeddings. MACUDA's multiple alignment method ensures that the mesoscale cross-day neural manifolds are aligned within a unified, stable manifold space. Then, the aligned data is fed into a multi-source domain adaptation decoder based on convolutional neural networks, thereby stably decoding macroscopic behavioral signals. In the application scenario of brain-computer interface Center-and-Out Reach (COR) tasks, extensive comparative experiments demonstrate the high generalization performance of the MACUDA method in cross-day spike trains decoding tasks, and internal ablation experiments prove the effectiveness of the multiple alignment approach in MACUDA.

Keyword离散时间动态系统 脑脉冲序列 脉冲自适应动态规划 脉冲神经网络 多尺度动力学 脑机接口
Language中文
Document Type学位论文
Identifierhttp://ir.ia.ac.cn/handle/173211/57187
Collection毕业生_博士学位论文
Recommended Citation
GB/T 7714
韩立元. 基于脑脉冲序列的离散时间动态系统学习控制研究[D],2024.
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