论文标题
未知强制输入的本地化和估计：组套索方法
Localization and Estimation of Unknown Forced Inputs: A Group LASSO Approach
论文作者
论文摘要
我们在未知的初始状态时对线性动力学系统的一组稀疏强迫输入进行建模和研究。这个问题与检测电力网络中的强制振荡特别重要。我们将测量值表示为一个添加剂模型，其中包括随时间分组的初始状态和输入，这两者都根据基础函数（即脉冲响应系数）进行扩展。使用此模型，具有概率保证，我们恢复了位置，并同时使用组Lasso的变体（线性绝对收缩和选择操作员）方法同时估算了初始状态并强迫输入。具体而言，我们提供了一个紧密的上限：（i）组套索估计器错误地识别源位置的可能性，以及（ii）估计误差的$ \ ell_2 $ -norm。我们的边界明确取决于测量范围的长度，噪声统计，输入和传感器的数量以及脉冲响应矩阵的奇异值。我们的理论分析是最早为在输入到输出延迟假设下的线性动力学系统的组LASSO估计器提供完整处理的方法之一。最后，我们验证了合成模型和IEEE 68总线16机械系统的结果。
We model and study the problem of localizing a set of sparse forcing inputs for linear dynamical systems from noisy measurements when the initial state is unknown. This problem is of particular relevance to detecting forced oscillations in electric power networks. We express measurements as an additive model comprising the initial state and inputs grouped over time, both expanded in terms of the basis functions (i.e., impulse response coefficients). Using this model, with probabilistic guarantees, we recover the locations and simultaneously estimate the initial state and forcing inputs using a variant of the group LASSO (linear absolute shrinkage and selection operator) method. Specifically, we provide a tight upper bound on: (i) the probability that the group LASSO estimator wrongly identifies the source locations, and (ii) the $\ell_2$-norm of the estimation error. Our bounds explicitly depend upon the length of the measurement horizon, the noise statistics, the number of inputs and sensors, and the singular values of impulse response matrices. Our theoretical analysis is one of the first to provide a complete treatment for the group LASSO estimator for linear dynamical systems under input-to-output delay assumptions. Finally, we validate our results on synthetic models and the IEEE 68-bus, 16-machine system.
