离散分数阶动态网络最小能量状态估计
Discrete-Time Fractional-Order Dynamical Networks Minimum-Energy State Estimation
摘要：
分数阶动态网络越来越多地被用于建模和描述过程，展示了长期记忆或复杂的交错的依赖关系之间的空间和时间组件的各种动态网络。值得注意的例子包括使用脑电图（EEG）或血氧水平依赖（BOLD）数据创建的联网控制系统或神经生理学网络。因此，分数阶动态网络的状态估计成为一个重要的问题。为此，本文讨论了离散时间分数阶动态网络（DT-FODN）的最小能量状态估计问题，其中状态和输出方程受被认为是确定性的、有界的和未知的加性噪声的影响。具体而言，我们推导出相应的估计，并表明所得到的估计误差是指数输入状态稳定的干扰和信号，这是随着所采用的近似模型的精度的增加而减少。一个说明性的例子表明，所提出的方法对现实世界的神经生理网络的有效性。
英文摘要：
Fractional-order dynamical networks are increasingly being used to model and describe processes demonstrating long-term memory or complex interlaced dependencies amongst the spatial and temporal components of a wide variety of dynamical networks. Notable examples include networked control systems or neurophysiological networks which are created using electroencephalographic (EEG) or blood-oxygen-level-dependent (BOLD) data. As a result, the estimation of the states of fractional-order dynamical networks poses an important problem. To this effect, this paper addresses the problem of minimum-energy state estimation for discrete-time fractional-order dynamical networks (DT-FODN), where the state and output equations are affected by an additive noise that is considered to be deterministic, bounded, and unknown. Specifically, we derive the corresponding estimator and show that the resulting estimation error is exponentially input-to-state stable with respect to the disturbances and to a signal that is decreasing with the increase of the accuracy of the adopted approximation model. An illustrative example shows the effectiveness of the proposed method on real-world neurophysiological networks.
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