论文标题
关于降低线性二次高斯控制器的控制器的性能界限
On Controller Reduction in Linear Quadratic Gaussian Control with Performance Bounds
论文作者
论文摘要
减少控制器的问题在控制理论方面具有丰富的历史。但是，许多问题仍然开放。特别是，在降低一般非观察者控制器和随后对闭环性能的量化阶段的顺序上，很少有结果。线性二次高斯（LQG）控制的无模型策略优化的最新发展突出了该问题的重要性。在本文中，我们首先提出了一组新的足够条件，以确保扰动的控制器保持内部稳定。基于此结果，我们说明了如何使用平衡的截断和模态截断来降低一般非观察者控制器的顺序。我们还为减少订单控制器的LQG性能提供了明确的界限。此外，对于单输入单输出（SISO）系统，我们通过截断不稳定模式引入了一种新的控制器还原技术。我们通过数值模拟说明了我们的理论结果。我们的结果将是设计直接的政策搜索算法的宝贵工具，用于控制部分观察结果。
The problem of controller reduction has a rich history in control theory. Yet, many questions remain open. In particular, there exist very few results on the order reduction of general non-observer based controllers and the subsequent quantification of the closed-loop performance. Recent developments in model-free policy optimization for Linear Quadratic Gaussian (LQG) control have highlighted the importance of this question. In this paper, we first propose a new set of sufficient conditions ensuring that a perturbed controller remains internally stabilizing. Based on this result, we illustrate how to perform order reduction of general non-observer based controllers using balanced truncation and modal truncation. We also provide explicit bounds on the LQG performance of the reduced-order controller. Furthermore, for single-input-single-output (SISO) systems, we introduce a new controller reduction technique by truncating unstable modes. We illustrate our theoretical results with numerical simulations. Our results will serve as valuable tools to design direct policy search algorithms for control problems with partial observations.
