发表机构
University of Michigan; Northeastern University（密歇根大学; 东北大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究线性动态状态反馈在协同镇定中的优势，证明其严格扩大可协同镇定系统集合，并开发路径积分算法，表明增加控制器记忆可扩大可行区域。
AI 中文摘要
协同镇定，即为多个系统设计一个能够同时镇定的单一控制器，是鲁棒控制和数据驱动控制中的一个基本问题。尽管任何可镇定的线性系统都允许存在一个镇定的线性静态状态反馈控制器，但这种等价性并不适用于协同镇定。特别是，存在一些系统集合，它们无法通过线性静态状态反馈实现协同镇定，但可以通过线性动态状态反馈实现协同镇定。在本文中，我们研究了控制器记忆在协同镇定中的作用。我们证明，对于标量系统和高维示例，线性动态状态反馈严格扩大了可协同镇定系统的集合，相比于静态反馈。同时，我们识别出即使使用动态控制器也无法克服的结构性限制。我们还开发了一种基于路径积分的算法，用于计算有限系统集合的协同镇定控制器。数值结果表明，增加控制器记忆会扩大可行的协同镇定区域。这些结果突显了控制器架构作为协同镇定中一个关键结构因素的作用，并对降低基于学习的控制的样本复杂度具有潜在意义。
英文摘要
Co-stabilization, i.e., designing a single controller that stabilizes multiple systems, is a fundamental problem in robust and data-driven control. While any stabilizable linear system admits a stabilizing linear static state feedback controller, this equivalence does not extend to co-stabilization. In particular, there exist system collections that cannot be co-stabilized by linear static state feedback but can be co-stabilized using linear dynamic state feedback. In this paper, we study the role of controller memory in co-stabilization. We show that linear dynamic state feedback strictly enlarges the set of co-stabilizable systems compared to static feedback, for both scalar systems and high-dimensional examples. At the same time, we identify structural limitations that cannot be overcome even with dynamic controllers. We also develop a path-integral-based algorithm for computing co-stabilizing controllers for a finite set of systems. Numerical results demonstrate that increasing controller memory enlarges the feasible co-stabilization region. These results highlight controller architecture as a key structural factor in co-stabilization, with potential implications for reducing the sample complexity of learning-based control.
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