论文标题
通过过滤稳定控制器及其基于LMI的计算的凸参数化
Convex Parameterization of Stabilizing Controllers and its LMI-based Computation via Filtering
论文作者
论文摘要
最近已经提出了稳定控制器的各种新的隐式参数化，这些参数允许允许对控制器施加结构约束。它们是凸，但无限维度，在频域中配制，没有可用的有效方法来计算。在本文中，我们介绍了Youla参数化的内核版本，以表征稳定控制器的集合。它具有单一的仿射约束，这使我们能够将控制器参数化作为一种新颖的鲁棒过滤问题。这使得可以得出稳定控制器的第一个有效线性矩阵不等式（LMI）隐式参数化。我们的LMI表征不仅可以接受有效的数值计算，而且还保证了一个有效的实用部署的全阶稳定动力控制器。数值实验表明，与现有的闭环参数化相比，我们的LMI可以更快地求解数量级。
Various new implicit parameterizations for stabilizing controllers that allow one to impose structural constraints on the controller have been proposed lately. They are convex but infinite-dimensional, formulated in the frequency domain with no available efficient methods for computation. In this paper, we introduce a kernel version of the Youla parameterization to characterize the set of stabilizing controllers. It features a single affine constraint, which allows us to recast the controller parameterization as a novel robust filtering problem. This makes it possible to derive the first efficient Linear Matrix Inequality (LMI) implicit parametrization of stabilizing controllers. Our LMI characterization not only admits efficient numerical computation, but also guarantees a full-order stabilizing dynamical controller that is efficient for practical deployment. Numerical experiments demonstrate that our LMI can be orders of magnitude faster to solve than the existing closed-loop parameterizations.
