Dynamic performance enhancement for nonlinear stochastic systems using RBF driven nonlinear compensation with extended Kalman filter

Zhou, Yuyang; Wang, Aiping; Zhou, Ping; Wang, Hong; Chai, Tianyou

doi:10.1016/j.automatica.2019.108693

Title: Dynamic performance enhancement for nonlinear stochastic systems using RBF driven nonlinear compensation with extended Kalman filter

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Abstract

Herein, a novel hybrid control method is proposed to enhance the tracking performance of the Proportional–Integral (PI) based control system for a class of nonlinear and non-Gaussian stochastic dynamic processes with unmeasurable states. The system performance is presented by tracking error entropy as the system is nonlinear and subjected to non-Gaussian noises. The well-known kernel density estimation (KDE) technique is employed to estimate the entropy because the precise statistical property of noises is not available for many industrial processes. Since in many industrial cases gains of PI controllers are fixed, a compensative controller is designed without changing the existing closed loop PI controller. Moreover, the compensative signal is formed using the estimated states from the extended Kalman filter (EKF) and a nonlinear compensation realized by the radial basis function (RBF) neural network. The weights of RBF are trained to minimize the entropy of the closed loop tracking error. The convergence of RBF network is discussed and the stability of the resulting closed-loop control system is analysed in mean square sense. Finally, two numerical examples and a practical system simulation are given to illustrate the effectiveness of the proposed control method.

Authors:

Zhou, Yuyang ^[1]; Wang, Aiping ^[2]; Zhou, Ping ^[3]; Wang, Hong ^[4]; Chai, Tianyou ^[3]

Univ. of Manchester (United Kingdom)
Bozhou Univ. (People's Republic of China); Anhui Univ. (PR China)
Northeastern Univ., Shenyang (People's Republic of China)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Publication Date:: Tue Dec 03 00:00:00 EST 2019

Research Org.:: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Sponsoring Org.:: USDOE; National Natural Science Foundation of China (NSFC)

OSTI Identifier:: 1607182

Grant/Contract Number:: AC05-00OR22725; 61890934; 61290323; 61333007

Resource Type:: Accepted Manuscript

Journal Name:: Automatica

Additional Journal Information:: Journal Volume: 112; Journal Issue: C; Journal ID: ISSN 0005-1098

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 42 ENGINEERING; Non-Gaussian stochastic nonlinear systems; Minimum entropy criterion; RBF neural network; Kernel density estimation; Extended Kalman filter; Tracking performance enhancement

Citation Formats


                    Zhou, Yuyang, Wang, Aiping, Zhou, Ping, Wang, Hong, and Chai, Tianyou. Dynamic performance enhancement for nonlinear stochastic systems using RBF driven nonlinear compensation with extended Kalman filter.  United States: N. p., 2019. 
Web.  doi:10.1016/j.automatica.2019.108693.

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                    Zhou, Yuyang, Wang, Aiping, Zhou, Ping, Wang, Hong, & Chai, Tianyou. Dynamic performance enhancement for nonlinear stochastic systems using RBF driven nonlinear compensation with extended Kalman filter.  United States.  https://doi.org/10.1016/j.automatica.2019.108693

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                    Zhou, Yuyang, Wang, Aiping, Zhou, Ping, Wang, Hong, and Chai, Tianyou. Tue .  
"Dynamic performance enhancement for nonlinear stochastic systems using RBF driven nonlinear compensation with extended Kalman filter".  United States.  https://doi.org/10.1016/j.automatica.2019.108693.  https://www.osti.gov/servlets/purl/1607182.

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@article{osti_1607182,

  title        = {Dynamic performance enhancement for nonlinear stochastic systems using RBF driven nonlinear compensation with extended Kalman filter},

  author       = {Zhou, Yuyang and Wang, Aiping and Zhou, Ping and Wang, Hong and Chai, Tianyou},

  abstractNote = {Herein, a novel hybrid control method is proposed to enhance the tracking performance of the Proportional–Integral (PI) based control system for a class of nonlinear and non-Gaussian stochastic dynamic processes with unmeasurable states. The system performance is presented by tracking error entropy as the system is nonlinear and subjected to non-Gaussian noises. The well-known kernel density estimation (KDE) technique is employed to estimate the entropy because the precise statistical property of noises is not available for many industrial processes. Since in many industrial cases gains of PI controllers are fixed, a compensative controller is designed without changing the existing closed loop PI controller. Moreover, the compensative signal is formed using the estimated states from the extended Kalman filter (EKF) and a nonlinear compensation realized by the radial basis function (RBF) neural network. The weights of RBF are trained to minimize the entropy of the closed loop tracking error. The convergence of RBF network is discussed and the stability of the resulting closed-loop control system is analysed in mean square sense. Finally, two numerical examples and a practical system simulation are given to illustrate the effectiveness of the proposed control method.},

  doi          = {10.1016/j.automatica.2019.108693},

  journal      = {Automatica},

  number       = C,

  volume       = 112,

  place        = {United States},

  year         = {Tue Dec 03 00:00:00 EST 2019},

  month        = {Tue Dec 03 00:00:00 EST 2019}

}

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