几类随机分数阶复杂网络的参数及状态估计问题研究

With the progress of fractional order calculus and network technique, stochastic fractional order complex networks have become a hot topic in the control field. This project will discuss the parameter and state estimation problems for several classes of stochastic fractional order complex networks. By summarizing the existing methods of characterizing the fractional order and stochastic systems, the mathematical models will be given for the newly stochastic fractional order systems. Considering the physical plant involving the features of nonlinear, time-varying as well as stochastic and the network-induced phenomena, the nonlinear stochastic fractional order dynamic models and measurement models will be established. For the linear and special nonlinear fractional order complex networks, the parameter estimation problems will be investigated firstly. By employing the techniques of Laplace transform, Chebyshev lemma and ergodic theory, the asymptotic properties, consistency and local asymptotic normality will be studied by a set of conditions. Subsequently, based on the augmented method and fractional order properties，the state estimators will be designed. And the dynamic performance will be analyzed for the error systems by Lyapunov functional, Hurwitz condition, LaSalle invariance principle. The effectiveness and applicability of the proposed estimation theory will be demonstrated by the computer numerical simulation. The theory on parameter estimation and state estimation of complex networks will be enriched by the investigation of this project.

随着网络技术和分数阶微积分的发展，随机分数阶复杂网络已成为控制领域中的研究热点。本项目研究几类随机分数阶复杂网络的参数及状态估计问题。首先归纳现有描述分数阶特性和随机现象的方法，建立刻画随机性、分数阶特性等系统结构特性的数学模型。综合考虑具有非线性性、时变性和随机性的物理对象及网络化诱导现象，建立相应随机分数阶动力学模型与测量模型。针对几类线性与特殊非线性随机分数阶复杂网络系统，首先给出对应的参数估计方法，利用Laplace变换、Chebyshev引理和遍历性定理等数学工具，分析参数估计误差的一致收敛性、相容性和渐近正态性。然后，基于分数阶微积分性质和系统增广方法构造状态估计器，应用Lyapunov泛函、Hurwitz判据、LaSalle不变原理等手段分析状态估计误差系统的动态性能。最终，通过计算机数值仿真模拟，验证所提出的估计方法及算法的有效性。本研究将丰富复杂网络的参数及状态估计理论。

本项目研究了复杂网络化环境下非线性随机系统的参数估计、状态估计、同步控制等问题。归纳了描述现有网络诱导现象的方法，建立刻画参数不确定、多重测量衰减、随机发生时变时滞、测量丢失等新型网络诱导现象的数学模型。综合考虑具有非线性性、时变性和随机性的物理对象及网络化诱导现象，建立了相应的非线性随机动力学模型与测量模型。给出了新的网络化时变随机系统的状态估计策略（方差受限状态估计、分布式状态估计、采样 H-infinity 状态估计等），提出了新的非线性时变网络化系统的控制和同步方法，分析网络化系统的稳定性等动态性能；此外，针对随机微分方程-Logistic扩散模型和一般非线性非时齐随机系统模型研究了其在离散观测情形下的未知参数估计问题，完成对似然率函数和极大似然估计量近似值的精确度分析，并分析了参数估计的渐近相合性及估计误差的局部渐近正态性,同时通过分析似然率随机域的弱收敛性进一步得到了Bernstein-Von- Mises有界定理成立的相应条件。本项目给出了保证算法鲁棒性、有界性等性能的充分性判别条件。本项目推动了网络化系统和非线性随机系统理论的进一步发展，研究成果为解决非线性网络化随机系统的分析和综合问题提供有效的理论与方法。.. 在本项目资助下，发表论文14篇，授权实用新型专利1项，软件著作权1项，并培养了一批优秀的研究生。