论文标题
线性参数变化子空间标识：统一框架
Linear Parameter-Varying Subspace Identification: A Unified Framework
论文作者
论文摘要
在本文中，我们为线性参数变化（LPV）系统的子空间识别（SID）建立了一个统一的框架，以创新形式估算LPV状态空间（SS）模型。该框架使我们能够得出新颖的LPV SID方案，这些方案是现有线性时间流动（LTI）方法的扩展。更具体地说，我们通过系统地建立LPV子空间识别理论来得出开放环，闭环和基于预测的数据方程，这是SS表示的输入输出替代形式。与LTI案例相比，我们显示了LPV设置的其他挑战。基于数据方程，提出了几种方法来基于最大样本或基于实现的参数估算LPV-SS模型。此外，已建立的LPV子空间识别问题已建立的理论框架使我们能够降低要估计的参数的数量，并克服相关矩阵的维度问题，从而导致LPV SIDS的计算复杂性降低。据作者所知，本文是对LPV子空间识别问题的第一次深入研究。在蒙特卡洛研究中，证明了提出的子空间识别方法的有效性，并与现有方法进行了比较，该研究识别基准MIMO LPV系统。
In this paper, we establish a unified framework for subspace identification (SID) of linear parameter-varying (LPV) systems to estimate LPV state-space (SS) models in innovation form. This framework enables us to derive novel LPV SID schemes that are extensions of existing linear time-invariant (LTI) methods. More specifically, we derive the open-loop, closed-loop, and predictor-based data-equations, an input-output surrogate form of the SS representation, by systematically establishing an LPV subspace identification theory. We show the additional challenges of the LPV setting compared to the LTI case. Based on the data-equations, several methods are proposed to estimate LPV-SS models based on a maximum-likelihood or a realization based argument. Furthermore, the established theoretical framework for the LPV subspace identification problem allows us to lower the number of to-be-estimated parameters and to overcome dimensionality problems of the involved matrices, leading to a decrease in the computational complexity of LPV SIDs in general. To the authors' knowledge, this paper is the first in-depth examination of the LPV subspace identification problem. The effectiveness of the proposed subspace identification methods are demonstrated and compared with existing methods in a Monte Carlo study of identifying a benchmark MIMO LPV system.
