基于多稳定性理论的神经网络预定性能控制研究

Multi-stability is basic mechanism for associative content-addressable memory storage and pattern recognition of human brain neural systems. However, it will make neural network be meta-stability by perturbation of initial value, changes of network parameters and coupling of neurons, i.e., leading to brain deseases. Recurrent neural network is the math model for human brain neural systems and parameters of network simulates the strength of neuron synapse. In this project, we take neural network model as research object, analyze the multi-stability of neural networks under perturbation of initial value, changes of network parameters and coupling of neurons and design the control law which can make the network state be convergent to the desired attractor, i.e., the prescribed performance control law. Firstly, we analyze the multi-stability of the traditional and memristive neural networks by using the state space division, limit set, invariant set, and differential inclusions theories under perturbation of initial value, changes of network parameters and coupling of neurons. Then we try to obtain numerical state information of traditional and memristive neural networks and design of prescribed performance control law by numerical calculation method, optimization algorithm and control theory. Finally, we present the prescribed performance control law design method corresponding to the given different attractors and the associative memory procedures based on neural networks with the precribed performance control law. The study of this project can provide some valuable theoretical references for the treatment of brain diseases such as Parkinson and epilepsy.

多稳定性是人脑神经系统联想内容寻址记忆存储与模式识别的基本机制，然而初始值扰动、网络络参数变化和神经元耦合变化会使得神经网络亚稳定，即导致脑疾病的发生。递归神经网络是人脑神经系统的数学模型，网络的参数模拟神经元突触强度，状态之间相互耦合。本项目以递归神经网络为研究对象，分析神经网络在初始值的扰动、网络参数的变化和神经元耦合变化下的多稳定性，设计能使得网络状态收敛到指定的吸引子的控制律，即预定性能控制律。首先利用状态空间剖分、极限集、不变集、以及微分包含理论分析传统和忆阻神经网络在初始值的扰动、网络参数的变化和神经元耦合变化下的多稳定性；接着用数值计算方法、优化算法及控制理论获取传统和忆阻神经网的状态信息并设计预定性能控制律；最后，给出不同给定吸引子所对应的预定性能控制律设计方法和基于带有预定控制律的神经网络的联想记忆设计程序。本项目的研究能为帕金森和癫痫等脑疾病的治疗提供有价值的理论参考。

研究了神经网络参数变化、外部输入扰动以及网络结构变化时的网络稳定性变化问题。进一步完善了神经网络在参数变化、外部输入扰动以及网络结构变化情形下的动力学理论分析方法，建立了一些神经网络区域稳定的代数判据。利用多稳定性理论分析方法以及状态空间剖技巧，给出了基于区域稳定的神经网络的联想记忆设计方法。注意到外部输入对稳定性和平衡点的影响，给出了神经网络全局区域稳定的充分条件。根据忆阻的数学模型，分析了忆阻及以忆阻作为连接权值的忆阻神经网络模型，同时给出了神经网络多稳定性条件以及用该网络实现联想记忆的程序，为了实现类脑智能计算和帕金森、癫痫等脑疾病的治疗提供了理论参考。. 主持项目期间加强相关领域的国内外合作。项目负责人先后担任了三个国际学术会议的程序委员会委员。该项目已正式发表标准基金资助的学术论文11篇，其中SCI收录的7篇。