标题： 具有噪声模型的线性、参数变化及非线性系统的高效识别 显示英文标题

标题： Efficient identification of linear, parameter-varying, and nonlinear systems with noise models

摘要： 我们提出了一种通用的系统辨识方法，能够估计广泛的状态空间动态模型，包括线性时不变（LTI）、线性参数变化（LPV）以及非线性（NL）动态模型，以及相当一般的噪声模型类别。 类似于LTI情况，我们证明了对于这一广义模型结构类（包括非线性情况），模型动力学可以分解为确定性过程和随机噪声部分，从而允许以无缝方式调节组合模型在非线性和噪声建模方面的复杂度。 我们通过人工神经网络（ANN）对涉及的非线性函数关系进行参数化，尽管也可以使用替代的参数化非线性映射。 为了估计由此产生的模型结构，我们优化了一个基于预测误差的准则，采用高效的约束拟牛顿法和自动微分相结合的方法，与现有最先进的ANN方法相比，训练时间达到秒级，而后者可能需要数小时来处理类似复杂度的模型。 我们正式建立了所提出方法的一致性保证，并在多个基准LTI、LPV和NL系统辨识问题上展示了其优越的估计精度和计算效率。 显示英文摘要

摘要： 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.