Online Identification of Nonlinear Stochastic Spatiotemporal System With Multiplicative Noise by Robust Optimal Control-Based Kernel Learning Method
Online Identification of Nonlinear Stochastic Spatiotemporal System With Multiplicative Noise by Robust Optimal Control-Based Kernel Learning Method
复制标题
基于鲁棒最优控制核学习方法的乘性噪声非线性随机时空系统在线辨识
DOI：
10.1109/tnnls.2018.2843883
复制
发表时间：
2019
影响因子：
10.4
通讯作者：
Jing Xingjian
中科院分区：
文献类型：
--
作者：
Ning Hanwen;Qing Guangyan;Tian Tianhai;Jing Xingjian
在本文中，我们提出了一种新的核方法的在线识别随机非线性时空动力系统的鲁棒控制方法。利用差分方法，将乘性噪声驱动的随机时空系统转化为一类具有非均匀随机项的多输入多输出部分线性核模型.借助于再生核Hilbert空间的技巧，在线学习问题被合理地看作是一组时变线性动态系统的输出反馈控制问题。我们开发了一个有效的算法来解决学习问题的PLKM和SST系统采用模型预测控制理论。与已有的学习方法相比，该方法对带乘性噪声的时空动力学具有自适应、鲁棒、快速收敛的在线建模性能，极大地方便了对系统物理特性的表征.此外，这项研究首次解决了SST系统的学习问题与新的鲁棒控制技术，这可以提供一些新的见解，从最优控制理论的角度设计核机器学习方法。基准系统的数值研究，以说明我们的新方法的有效性和效率。
In this paper, we propose a novel kernel method for the online identification of stochastic nonlinear spatiotemporal dynamical systems using the robust control approach. By the difference method, the stochastic spatiotemporal (SST) systems driven by multiplicative noise are first transformed into a class of multi-input-multi-output-partially linear kernel models (PLKMs) with heterogeneous random terms. With the help of techniques established for reproducing kernel Hilbert space, the online learning problem is reasonably considered as an output feedback control problem for a group of time varying linear dynamical systems. We develop an effective algorithm to address the learning problem of PLKM and SST systems by employing the model predictive control theory. Compared with the existing learning methods, the new one can achieve adaptive, robust, and fast convergent online modeling performance for the spatiotemporal dynamics with multiplicative noise, which greatly facilitates the characterization of physical characteristics of the system. Moreover, this investigation for the first time addresses the learning problems for SST systems with novel robust control techniques, which can provide some novel insights into the design of kernel machine learning methods from the perspective of optimal control theory. Numerical studies for benchmark systems are presented to illustrate the effectiveness and efficiency of our new method.