基于分组原子范数正则化的线性时周期系统辨识
Linear Time-Periodic System Identification with Grouped Atomic Norm Regularization
摘要：
本文提出了一种新的线性时间周期（LTP）系统辨识方法。与以前的方法，完全分离的动态在不同的标签时间进行识别，该方法侧重于施加适当的结构约束的线性时不变（LTI）的LTP系统的重新制定。该方法采用线性时变系统的切换截断无限脉冲响应模型，其中结构约束被解释为要求所有子模型的非截断模型的极点位于相同的位置。这种约束是通过将LTI系统的原子范数正则化框架与回归中的组套索技术相结合来施加的。因此，估计的系统是一致的和低阶的，这是很难实现与其他现有的估计器。MonteCarlo模拟表明，分组原子范数方法不仅比其他正则化方法具有更好的结果，而且在高噪声水平下的模型拟合性能也优于子空间辨识方法。
英文摘要：
This paper proposes a new methodology in linear time-periodic (LTP) system identification. In contrast to previous methods that totally separate dynamics at different tag times for identification, the method focuses on imposing appropriate structural constraints on the linear time-invariant (LTI) reformulation of LTP systems. This method adopts a periodically-switched truncated infinite impulse response model for LTP systems, where the structural constraints are interpreted as the requirement to place the poles of the non-truncated models at the same locations for all sub-models. This constraint is imposed by combining the atomic norm regularization framework for LTI systems with the group lasso technique in regression. As a result, the estimated system is both uniform and low-order, which is hard to achieve with other existing estimators. Monte Carlo simulation shows that the grouped atomic norm method does not only show better results compared to other regularized methods, but also outperforms the subspace identification method under high noise levels in terms of model fitting.
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