论文标题
带有混合乘法和加性噪声的离散时间线性系统的协方差转向
Covariance Steering of Discrete-Time Linear Systems with Mixed Multiplicative and Additive Noise
论文作者
论文摘要
在本文中，我们研究了具有乘法和附加噪声的离散时间线性系统的协方差转向（CS）问题。具体而言，我们考虑了所谓的CS问题的两个变体。第一个问题的目的（称为确切的CS问题）是在有限的时间内将状态过程的平均值和协方差转向其所需值。在第二个被称为“放松”的CS问题的情况下，协方差分配约束被放松成积极的半明确约束。我们表明，在应用合适的可变变换和约束放松后，可以将放松的CS问题作为等效凸半准计划（SDP）施加。此外，我们基于放松的问题公式提出了针对精确CS问题的两步解决方案程序，如果存在一个问题，该问题将返回可行的解决方案。最后，提供了数值实验的结果，以显示提出的解决方案方法的功效。
In this paper, we study the covariance steering (CS) problem for discrete-time linear systems subject to multiplicative and additive noise. Specifically, we consider two variants of the so-called CS problem. The goal of the first problem, which is called the exact CS problem, is to steer the mean and the covariance of the state process to their desired values in finite time. In the second one, which is called the ``relaxed'' CS problem, the covariance assignment constraint is relaxed into a positive semi-definite constraint. We show that the relaxed CS problem can be cast as an equivalent convex semi-definite program (SDP) after applying suitable variable transformations and constraint relaxations. Furthermore, we propose a two-step solution procedure for the exact CS problem based on the relaxed problem formulation which returns a feasible solution, if there exists one. Finally, results from numerical experiments are provided to show the efficacy of the proposed solution methods.
