论文标题
马尔可夫参数估计和系统标识中的多个射击目标的可能性概括
Likelihood-based generalization of Markov parameter estimation and multiple shooting objectives in system identification
论文作者
论文摘要
本文考虑了来自嘈杂和稀疏数据的线性和非线性非自治系统的系统识别（ID）问题。我们提出和分析源自贝叶斯公式的目标函数，以学习具有随机动力学的隐藏的马尔可夫模型。然后，我们在线性和非线性系统ID的几种最新方法中分析了此目标功能。在前者中，我们分析了Markov参数估计的最小二乘方法，在后者中，我们分析了多个射击方法。我们通过证明它们可以看作是在某些简化的假设下被视为所提出的优化目标的特殊情况：数据的有条件独立性和零模型误差的特殊情况，从而证明了这些现有方法所带来的优化问题的局限性。此外，我们观察到，我们提出的方法改善了平滑度和固有的正则化，使其非常适合系统ID，并为这些特征的起源提供了数学解释。最后，与数据嘈杂和/或稀疏相比，数值模拟显示出比多次拍摄的平均误差超过8.7倍。此外，即使参数多于数据，或者底层系统表现出混乱的行为时，提出的方法也可以识别准确且可推广的模型。
This paper considers the problem of system identification (ID) of linear and nonlinear non-autonomous systems from noisy and sparse data. We propose and analyze an objective function derived from a Bayesian formulation for learning a hidden Markov model with stochastic dynamics. We then analyze this objective function in the context of several state-of-the-art approaches for both linear and nonlinear system ID. In the former, we analyze least squares approaches for Markov parameter estimation, and in the latter, we analyze the multiple shooting approach. We demonstrate the limitations of the optimization problems posed by these existing methods by showing that they can be seen as special cases of the proposed optimization objective under certain simplifying assumptions: conditional independence of data and zero model error. Furthermore, we observe that our proposed approach has improved smoothness and inherent regularization that make it well-suited for system ID and provide mathematical explanations for these characteristics' origins. Finally, numerical simulations demonstrate a mean squared error over 8.7 times lower compared to multiple shooting when data are noisy and/or sparse. Moreover, the proposed approach can identify accurate and generalizable models even when there are more parameters than data or when the underlying system exhibits chaotic behavior.
