提出最优中心激励方法，实现线性系统辨识的最少样本需求。
Optimal Centered Active Excitation in Linear System Identification
- 基于最小二乘与半定规划设计主动学习算法
- 理论证明样本复杂度下界与上界一致，仅差常数因子
- 适用于高维系统建模，可高效估计系统矩阵
我们提出一种针对线性系统辨识的主动学习算法，采用最优中心噪声激励。该算法基于普通最小二乘法和半定规划，可在保证最低样本复杂度的前提下，高效计算系统矩阵的估计。首先，我们建立了任何主动学习算法在指定精度与置信水平下的样本复杂度下界；其次，推导出所提算法的样本复杂度上界，该上界与任意算法的下界仅相差一个通用常数因子。我们的紧致边界易于解释，并明确展示了其对系统参数（如状态维度）的依赖关系。
原文摘要 · Abstract (English)
We propose an active learning algorithm for linear system identification with optimal centered noise excitation. Notably, our algorithm, based on ordinary least squares and semidefinite programming, attains the minimal sample complexity while allowing for efficient computation of an estimate of a system matrix. More specifically, we first establish lower bounds of the sample complexity for any active learning algorithm to attain the prescribed accuracy and confidence levels. Next, we derive a sample complexity upper bound of the proposed algorithm, which matches the lower bound for any algorithm up to universal factors. Our tight bounds are easy to interpret and explicitly show their dependence on the system parameters such as the state dimension.
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