Data-driven distribution tracking for stochastic non-linear systems via PID design

Qichun Zhang, Hong Yue

Research output: Contribution to conferencePaper

Abstract

This paper investigates the stochastic distribution tracking problem while the probability density function (PDF) of the stochastic non-linear system output can be controlled to desired distribution. To achieve the control objective, a data-driven approach is proposed in which no information of the system model is required. The output PDF can be estimated by kernel density estimation (KDE) based on the collected system output data. Using the estimated PDF, the probability states can be obtained by sampling operation which can be used to re-characterise the PDF of the system output. Thus, the tracking performance can be achieved by PID control. The parametric selection of the controller has been analysed following the identified PDF dynamic model to assure the convergence of the system output. The effectiveness of the presented algorithm is illustrated by a numerical example.

Conference

Conference25th IEEE International Conference on Automation and Computing
CountryUnited Kingdom
CityLancaster
Period5/09/197/09/19
Internet address

Fingerprint

Probability density function
Nonlinear systems
Three term control systems
Dynamic models
Sampling
Controllers

Keywords

  • stochastic distribution control
  • non-Gaussian systems
  • probability density function (PDF)
  • data-driven
  • PID

Cite this

Zhang, Q., & Yue, H. (Accepted/In press). Data-driven distribution tracking for stochastic non-linear systems via PID design. 16-21. Paper presented at 25th IEEE International Conference on Automation and Computing, Lancaster, United Kingdom.
Zhang, Qichun ; Yue, Hong. / Data-driven distribution tracking for stochastic non-linear systems via PID design. Paper presented at 25th IEEE International Conference on Automation and Computing, Lancaster, United Kingdom.6 p.
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abstract = "This paper investigates the stochastic distribution tracking problem while the probability density function (PDF) of the stochastic non-linear system output can be controlled to desired distribution. To achieve the control objective, a data-driven approach is proposed in which no information of the system model is required. The output PDF can be estimated by kernel density estimation (KDE) based on the collected system output data. Using the estimated PDF, the probability states can be obtained by sampling operation which can be used to re-characterise the PDF of the system output. Thus, the tracking performance can be achieved by PID control. The parametric selection of the controller has been analysed following the identified PDF dynamic model to assure the convergence of the system output. The effectiveness of the presented algorithm is illustrated by a numerical example.",
keywords = "stochastic distribution control, non-Gaussian systems, probability density function (PDF), data-driven, PID",
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Zhang, Q & Yue, H 2019, 'Data-driven distribution tracking for stochastic non-linear systems via PID design' Paper presented at 25th IEEE International Conference on Automation and Computing, Lancaster, United Kingdom, 5/09/19 - 7/09/19, pp. 16-21.

Data-driven distribution tracking for stochastic non-linear systems via PID design. / Zhang, Qichun; Yue, Hong.

2019. 16-21 Paper presented at 25th IEEE International Conference on Automation and Computing, Lancaster, United Kingdom.

Research output: Contribution to conferencePaper

TY - CONF

T1 - Data-driven distribution tracking for stochastic non-linear systems via PID design

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AU - Yue, Hong

N1 - © 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

PY - 2019/6/21

Y1 - 2019/6/21

N2 - This paper investigates the stochastic distribution tracking problem while the probability density function (PDF) of the stochastic non-linear system output can be controlled to desired distribution. To achieve the control objective, a data-driven approach is proposed in which no information of the system model is required. The output PDF can be estimated by kernel density estimation (KDE) based on the collected system output data. Using the estimated PDF, the probability states can be obtained by sampling operation which can be used to re-characterise the PDF of the system output. Thus, the tracking performance can be achieved by PID control. The parametric selection of the controller has been analysed following the identified PDF dynamic model to assure the convergence of the system output. The effectiveness of the presented algorithm is illustrated by a numerical example.

AB - This paper investigates the stochastic distribution tracking problem while the probability density function (PDF) of the stochastic non-linear system output can be controlled to desired distribution. To achieve the control objective, a data-driven approach is proposed in which no information of the system model is required. The output PDF can be estimated by kernel density estimation (KDE) based on the collected system output data. Using the estimated PDF, the probability states can be obtained by sampling operation which can be used to re-characterise the PDF of the system output. Thus, the tracking performance can be achieved by PID control. The parametric selection of the controller has been analysed following the identified PDF dynamic model to assure the convergence of the system output. The effectiveness of the presented algorithm is illustrated by a numerical example.

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Zhang Q, Yue H. Data-driven distribution tracking for stochastic non-linear systems via PID design. 2019. Paper presented at 25th IEEE International Conference on Automation and Computing, Lancaster, United Kingdom.