Online Identification of Nonlinear Stochastic Spatiotemporal System with Multiplicative Noise by Robust Optimal Control-Based Kernel Learning Method

Hanwen Ning, Guangyan Qing, Tianhai Tian, Xingjian Jing

Research output: Journal article publicationJournal articleAcademic researchpeer-review

7 Citations (Scopus)


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.

Original languageEnglish
Article number8399841
Pages (from-to)389-404
Number of pages16
JournalIEEE Transactions on Neural Networks and Learning Systems
Issue number2
Publication statusPublished - 1 Feb 2019


  • Model predictive control (MPC)
  • multiplicative noise
  • online learning
  • partially linear kernel models (PLKMs)
  • spatiotemporal systems
  • system identification

ASJC Scopus subject areas

  • Software
  • Computer Science Applications
  • Computer Networks and Communications
  • Artificial Intelligence

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