论文标题
使用深层编码器网络的非线性状态空间识别
Nonlinear state-space identification using deep encoder networks
论文作者
论文摘要
动态系统的非线性状态空间识别通常是通过最小化模拟误差以减少模型误差的效果来执行的。对于大型数据集而言，此优化问题在计算上变得昂贵。此外，问题也是强烈的非凸，通常会导致亚最佳参数估计值。本文引入了一种方法，该方法通过将数据集分为多个独立部分，类似于多个拍摄方法，从而近似模拟损失。这种分裂操作允许使用随机梯度优化方法，该方法随数据集大小而良好地扩展，并对非凸成本函数具有平滑作用。本文的主要贡献是引入编码器函数来估计每个部分开始时的初始状态。编码器函数使用从历史输入和输出样本开始的馈送神经网络估算初始状态。在两个众所周知的基准上说明了所提出的状态空间编码方法的效率和性能，例如，该方法在Wiener-Hammerstein基准上实现了最低的已知模拟误差。
Nonlinear state-space identification for dynamical systems is most often performed by minimizing the simulation error to reduce the effect of model errors. This optimization problem becomes computationally expensive for large datasets. Moreover, the problem is also strongly non-convex, often leading to sub-optimal parameter estimates. This paper introduces a method that approximates the simulation loss by splitting the data set into multiple independent sections similar to the multiple shooting method. This splitting operation allows for the use of stochastic gradient optimization methods which scale well with data set size and has a smoothing effect on the non-convex cost function. The main contribution of this paper is the introduction of an encoder function to estimate the initial state at the start of each section. The encoder function estimates the initial states using a feed-forward neural network starting from historical input and output samples. The efficiency and performance of the proposed state-space encoder method is illustrated on two well-known benchmarks where, for instance, the method achieves the lowest known simulation error on the Wiener--Hammerstein benchmark.
