鲁棒正不变集的数据驱动综合：从状态反馈到输出反馈
Data-Driven Synthesis of Robust Positively Invariant Sets: From State Feedback to Output Feedback
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中文总结 AI 辅助
本文针对未知线性时不变系统，提出一种直接数据驱动框架，可通过半定规划从含噪声离线数据中综合状态反馈和基于观测器输出反馈场景下的鲁棒正不变集，避免中间模型相关步骤，数值示例验证了方法有效性。
中文摘要 AI 辅助
本文针对未知线性时不变系统，在状态反馈和基于观测器的输出反馈场景下，开发了一种用于鲁棒正不变（RPI）集综合的直接数据驱动框架。通过求解半定规划（SDP），可从含噪声的离线数据中直接综合反馈增益、观测器增益以及RPI集，避免了中间模型辨识或显式模型不确定集的构建。在状态反馈场景中，首先计算线性二次（LQ）型反馈增益，随后为所得闭环动力学综合椭球型RPI集；在基于观测器的输出反馈场景中，通过增广状态形式，利用离线数据计算观测器增益及对应系统状态的RPI集。该设计为两种场景下的不变集计算提供了统一方法，且直接数据驱动公式避免了中间模型不确定集的显式构建与传播。数值示例验证了所提方法的有效性。
英文摘要
This paper develops a direct data-driven framework for robust positively invariant (RPI) set synthesis for unknown linear time-invariant systems under state-feedback and observer-based output-feedback scenarios. The feedback and observer gains, along with the RPI sets, are directly synthesized from noisy offline data by solving semidefinite programs (SDPs), avoiding intermediate model identification or explicit model-uncertainty set construction. In the state-feedback case, a linear-quadratic (LQ)-type feedback gain is first computed, and an ellipsoidal RPI set is then synthesized for the resulting closed-loop dynamics. In the observer-based output-feedback case, offline data are used to compute the observer gain and the corresponding RPI set for the system state through an augmented-state formulation. This design provides a unified method for invariant-set computation in both scenarios, and the direct data-driven formulation avoids the explicit construction and propagation of an intermediate model-uncertainty set. Numerical examples illustrate the effectiveness of the proposed method.
