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: Contribution to journalArticleResearchpeer-review

Abstract

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
Volume30
Issue number2
DOIs
Publication statusPublished - 1 Feb 2019

Keywords

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

Cite this

@article{5d52e249ba914351a75ff4dc900c0795,
title = "Online Identification of Nonlinear Stochastic Spatiotemporal System with Multiplicative Noise by Robust Optimal Control-Based Kernel Learning Method",
abstract = "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.",
keywords = "Model predictive control (MPC), multiplicative noise, online learning, partially linear kernel models (PLKMs), spatiotemporal systems, system identification",
author = "Hanwen Ning and Guangyan Qing and Tianhai Tian and Xingjian Jing",
year = "2019",
month = "2",
day = "1",
doi = "10.1109/TNNLS.2018.2843883",
language = "English",
volume = "30",
pages = "389--404",
journal = "IEEE Transactions on Neural Networks and Learning Systems",
issn = "2162-237X",
number = "2",

}

Online Identification of Nonlinear Stochastic Spatiotemporal System with Multiplicative Noise by Robust Optimal Control-Based Kernel Learning Method. / Ning, Hanwen; Qing, Guangyan; Tian, Tianhai; Jing, Xingjian.

In: IEEE Transactions on Neural Networks and Learning Systems, Vol. 30, No. 2, 8399841, 01.02.2019, p. 389-404.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Online Identification of Nonlinear Stochastic Spatiotemporal System with Multiplicative Noise by Robust Optimal Control-Based Kernel Learning Method

AU - Ning, Hanwen

AU - Qing, Guangyan

AU - Tian, Tianhai

AU - Jing, Xingjian

PY - 2019/2/1

Y1 - 2019/2/1

N2 - 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.

AB - 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.

KW - Model predictive control (MPC)

KW - multiplicative noise

KW - online learning

KW - partially linear kernel models (PLKMs)

KW - spatiotemporal systems

KW - system identification

UR - http://www.scopus.com/inward/record.url?scp=85049357319&partnerID=8YFLogxK

U2 - 10.1109/TNNLS.2018.2843883

DO - 10.1109/TNNLS.2018.2843883

M3 - Article

VL - 30

SP - 389

EP - 404

JO - IEEE Transactions on Neural Networks and Learning Systems

JF - IEEE Transactions on Neural Networks and Learning Systems

SN - 2162-237X

IS - 2

M1 - 8399841

ER -