来自数据的全局认证不变椭球控制
Globally Certified Invariant-Ellipsoid Control from Data
- ITMO University（伊托莫大学）
- University of Sheffield（谢菲尔德大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出一种数据驱动方法，通过优化不变椭球参数设计状态反馈，利用值迭代与控制器评估界定成本，保证有限步内获得全局认证的近似最优镇定增益。
AI中文摘要：
本文提出了一种基于数据的方法，用于设计受有界扰动影响的离散时间线性系统的状态反馈。对于每个可容许的反馈增益和标量设计参数，李雅普诺夫方程确定一个不变椭球：一个在允许扰动下状态不能离开的区域。我们优化增益和参数以最小化由此产生的输出封闭的基于迹的度量。在每个参数值处，值迭代给出一个较低的成本界，而单独的控制器评估给出一个可达到的上界。这些界还使我们能够评估整个参数区间，而无需评估每个点。我们证明了搜索在有限次评估后停止，并得到一个镇定状态反馈增益，其目标在所选椭球族的下确界的任何指定绝对容差内。既不假设初始镇定增益，也不假设达到下确界。该保证假设精确算术和足够信息量的精确测量批次，包括数据收集期间的扰动；所得反馈仅使用状态。一个位置-速度示例说明了界、控制器检查和计算成本。
英文摘要：
This letter develops a data-based method for designing state feedback for a discrete-time linear system under bounded disturbances. For each admissible feedback gain and scalar design parameter, a Lyapunov equation determines an invariant ellipsoid: a region that the state cannot leave under the permitted disturbances. We optimise the gain and parameter to minimise a trace-based measure of the resulting output enclosure. At each parameter value, value iteration gives a lower cost bound, while separate controller evaluation gives an achievable upper bound. These bounds also let us assess whole parameter intervals without evaluating every point. We prove that the search stops after finitely many evaluations with a stabilising state-feedback gain whose objective is within any prescribed absolute tolerance of the infimum over the chosen ellipsoid family. Neither an initially stabilising gain nor attainment of the infimum is assumed. The guarantee assumes exact arithmetic and a sufficiently informative batch of exact measurements, including disturbances during data collection; the resulting feedback uses only the state. A position--velocity example illustrates the bounds, controller checks, and computational cost.
