Approximating the nearest stable discrete-time system
Approximating the nearest stable discrete-time system
复制标题
逼近最近的稳定离散时间系统
DOI：
10.1016/j.laa.2019.03.014
复制
发表时间：
2018
影响因子：
1.1
通讯作者：
Punit Sharma
中科院分区：
文献类型：
--
作者：
Nicolas Gillis;M. Karow;Punit Sharma
本文考虑了通过计算一个稳定矩阵到一个不稳定矩阵的邻域来镇定离散线性系统的问题。为此，我们提供了一个新的稳定矩阵集的特征。我们证明了矩阵A是稳定的当且仅当它可以写成A= S− 1 U B S，其中S是正定的，U是正交的，B是半正定压缩（即B的奇异值小于或等于1）。这个特征导致了一个等价的非凸优化问题，该问题具有一个易于投影的可行集。我们提出了一个非常有效的快速投影梯度方法来处理变量（S，U，B）的问题，并产生局部最优解。我们所提出的方法相比，其他方法的有效性。
In this paper, we consider the problem of stabilizing discrete-time linear systems by computing a nearby stable matrix to an unstable one. To do so, we provide a new characterization for the set of stable matrices. We show that a matrix A is stable if and only if it can be written as A= S− 1 U B S, where S is positive definite, U is orthogonal, and B is a positive semidefinite contraction (that is, the singular values of B are less or equal to 1). This characterization results in an equivalent non-convex optimization problem with a feasible set on which it is easy to project. We propose a very efficient fast projected gradient method to tackle the problem in variables (S, U, B) and generate locally optimal solutions. We show the effectiveness of the proposed method compared to other approaches.