统一建模各类动态系统，高效准确识别非线性与噪声结构。
Efficient identification of linear, parameter-varying, and nonlinear systems with noise models
- 用神经网络建模非线性关系，分离确定性与随机噪声部分。
- 训练仅需数秒，比现有方法快数小时，精度更高。
- 适用于线性、参数时变及非线性系统，适合工程建模场景。
我们提出一种通用系统辨识方法，可估计包括线性时不变（LTI）、线性参数时变（LPV）和非线性（NL）动态在内的广泛状态空间模型，并支持多类噪声模型。类似LTI情况，我们证明该类模型可分解为确定性过程与随机噪声部分，从而在非线性程度和噪声建模复杂度上实现无缝调节。通过人工神经网络（ANN）参数化非线性映射，也可使用其他参数化方式。采用基于预测误差的准则，结合约束拟牛顿法与自动微分，实现高效优化，训练时间在秒级，显著优于现有基于ANN的方法（需数小时）。我们正式建立了方法的一致性保证，并在多个基准测试中验证其在LTI、LPV和NL系统辨识中的高精度与高效率。
原文摘要 · Abstract (English)
We present a general system identification procedure capable of estimating of a broad spectrum of state-space dynamical models, including linear time-invariant (LTI), linear parameter-varying} (LPV), and nonlinear (NL) dynamics, along with rather general classes of noise models. Similar to the LTI case, we show that for this general class of model structures, including the NL case, the model dynamics can be separated into a deterministic process and a stochastic noise part, allowing to seamlessly tune the complexity of the combined model both in terms of nonlinearity and noise modeling. We parameterize the involved nonlinear functional relations by means of artificial neural-networks (ANNs), although alternative parametric nonlinear mappings can also be used. To estimate the resulting model structures, we optimize a prediction-error-based criterion using an efficient combination of a constrained quasi-Newton approach and automatic differentiation, achieving training times in the order of seconds compared to existing state-of-the-art ANN methods which may require hours for models of similar complexity. We formally establish the consistency guarantees for the proposed approach and demonstrate its superior estimation accuracy and computational efficiency on several benchmark LTI, LPV, and NL system identification problems.
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