从单条输入输出轨迹中识别部分可观测双线性系统参数
Finite Sample Identification of Partially Observed Bilinear Dynamical Systems
- 通过回归高度相关、非线性且重尾的协变量学习系统马尔可夫类参数
- 在统一稳定性假设下，给出高概率误差界，验证算法有效性
- 适用于需低样本量建模复杂动态系统的控制与系统识别场景
我们研究从噪声输入-输出数据中学习部分可观测双线性动力系统（BLDS）实现的问题。基于单条输入-输出轨迹，我们对学习系统马尔可夫类参数提供了有限时间分析，并由此获得系统的平衡实现。所提出的双线性系统辨识算法通过将输出回归到高度相关、非线性且重尾的协变量，来学习系统参数。此外，BLDS的稳定性依赖于激励系统的输入序列，这一特性为算法分析带来显著挑战。本文在统一稳定性假设下，建立了识别算法的高概率误差界。分析揭示了影响学习精度与样本复杂度的系统理论量。最后，通过合成数据的数值实验验证了这些见解。
原文摘要 · Abstract (English)
We consider the problem of learning a realization of a partially observed bilinear dynamical system (BLDS) from noisy input-output data. Given a single trajectory of input-output samples, we provide a finite time analysis for learning the system's Markov-like parameters, from which a balanced realization of the bilinear system can be obtained. Our bilinear system identification algorithm learns the system's Markov-like parameters by regressing the outputs to highly correlated, nonlinear, and heavy-tailed covariates. Moreover, the stability of BLDS depends on the sequence of inputs used to excite the system. These properties, unique to partially observed bilinear dynamical systems, pose significant challenges to the analysis of our algorithm for learning the unknown dynamics. We address these challenges and provide high probability error bounds on our identification algorithm under a uniform stability assumption. Our analysis provides insights into system theoretic quantities that affect learning accuracy and sample complexity. Lastly, we perform numerical experiments with synthetic data to reinforce these insights.
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