分数阶随机神经网络系统的分析与不连续控制

Taking the stochastic factors and fractional calculus into account, the system under consideration becomes fractional stochastic neural network systems, which is advanced and can more accurately simulate the real dynamic behavior of neurons. In this project, we are to study the stability and discontinuous synchronization control of fractional stochastic neural networks based on the vector Lyapunov function method. The relationship between Lyapunov functions and fractional stochastic neural network systems will investigate by stochastic analysis and fractional order calculus technique. The fractional order vector Halandy inequality with structure compatible with the systems will be established using the the Laplace transform and matrix analysis technique.Combined with stochastic analysis technique, stability criteria in different stochastic senses will be established by means of the vector Halandy inequality. Based on the discontinuous control strategy, the synchronization controller will be designed by virtue of non-smooth analysis and switching system theorem. The advantages of fractional derivatives and neural networks in image processing will be integrated，some new algorithm based on fractional stochastic neural network will be provided. This project will develop the theory of fractional stochastic system，and will help to probe the dynamics mechanism of fractional stochastic neural network system, and will initiate the new idea of study on analysis and synchronization control of fractional stochastic neural network systems.

分数阶导数更能准确地模拟神经元的真实的动力学行为，同时随机干扰必然会对网络的功能产生重要的影响，将随机因素和分数阶微积分同时考虑进来，研究随机分数阶神经网络具有重要的理论意义和现实价值。本项目基于向量Lyapunov函数方法对随机分数阶神经网络的稳定性与不连续同步控制进行研究： 运用随机分析及分数阶微积分理论建立Lyapunov函数与分数阶随机神经网络间的关系；运用非线性分析及Laplace变换技术，建立与神经网络结构相兼容的分数阶向量Halandy不等式，并结合随机分析技术研究分数阶随机神经网络不同随机意义下的稳定性问题；运用非光滑分析及切换系统理论，设计基于不连续控制策略同步控制器；并将分数阶微积分和神经网络在图像处理上的相整合。本项目将发展分数阶随机系统的理论，揭示分数阶随机神经网络系统动力学机理，为研究分数阶随机神经网络系统的分析与控制提供新的方法、新途径。

研究团队以“分数阶随机神经网络系统的分析与不连续控制”为中心，从1）基于向量Lyapunov函数的稳定性分析方法，2）随机系统及分数阶神经网络的稳定性，3）基于不连续控制的分数阶神经网络同步定和整数阶系统的随机镇定，4）事件触发机制下确定性网络的同步定及一致性控制，5）分数阶随机系统最优控制，共五个方面展开研究。获得了基于自适应动态规划算法的分数阶随机系统最优控制实现方案，基于向量Lyapunov函数的网络系统分析方法，基于间歇的混杂随机镇定策略的分析方法，基于间歇、脉冲、采样等不连续策略的分数神经网络同步定的系列成果，基于事件触发机制的网络的同步定及一致性判据。该研究首次给出了分数阶随机系统的最优控制的实现方案，丰富了随机系统和分数阶系统的分析方法，发展了基于不连续控制的网络系统同步定控制方法。