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

Qichun Zhang; Hong Yue

doi:10.23919/IConAC.2019.8895165

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

Qichun Zhang, Hong Yue

Electronic And Electrical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

1 Citation (Scopus)

13 Downloads (Pure)

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.

Original language	English
Title of host publication	2019 25th International Conference on Automation and Computing (ICAC)
Place of Publication	Piscataway, NJ.
Publisher	IEEE
Pages	16-21
Number of pages	6
ISBN (Electronic)	9781861376664
ISBN (Print)	9781861376657
DOIs	https://doi.org/10.23919/IConAC.2019.8895165
Publication status	Published - 11 Nov 2019
Event	25th IEEE International Conference on Automation and Computing - Lancaster, United Kingdom Duration: 5 Sept 2019 → 7 Sept 2019 http://www.cacsuk.co.uk/index.php/conferences/icac

Conference

Conference	25th IEEE International Conference on Automation and Computing
Country/Territory	United Kingdom
City	Lancaster
Period	5/09/19 → 7/09/19
Internet address	http://www.cacsuk.co.uk/index.php/conferences/icac

Keywords

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

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10.23919/IConAC.2019.8895165

Zhang-Yue-ICAC2019-Data-driven-distribution-tracking-for-stochastic-non-linear-systemsAccepted author manuscript, 854 KB

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title = "Data-driven distribution tracking for stochastic non-linear systems via PID design",

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",

author = "Qichun Zhang and Hong Yue",

note = "{\textcopyright} 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.; 25th IEEE International Conference on Automation and Computing ; Conference date: 05-09-2019 Through 07-09-2019",

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language = "English",

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AU - Zhang, Qichun

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 - 2019/11/11

Y1 - 2019/11/11

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.

KW - stochastic distribution control

KW - non-Gaussian systems

KW - probability density function (PDF)

KW - data-driven

KW - PID

U2 - 10.23919/IConAC.2019.8895165

DO - 10.23919/IConAC.2019.8895165

M3 - Conference contribution book

SN - 9781861376657

SP - 16

EP - 21

BT - 2019 25th International Conference on Automation and Computing (ICAC)

PB - IEEE

CY - Piscataway, NJ.

T2 - 25th IEEE International Conference on Automation and Computing

Y2 - 5 September 2019 through 7 September 2019

ER -

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

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Keywords

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