An Error-Entropy Minimization Algorithm for Tracking Control of Nonlinear Stochastic Systems with Non-Gaussian Variables

Yunlong Liu; Aiping Wang; Lei Guo; Hong Wang

doi:10.1016/j.ifacol.2017.08.1720

An Error-Entropy Minimization Algorithm for Tracking Control of Nonlinear Stochastic Systems with Non-Gaussian Variables

Yunlong Liu, Aiping Wang, Lei Guo, Hong Wang

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

This paper presents an error-entropy minimization tracking control algorithm for a class of dynamic stochastic systems. The system is represented by a set of time-varying discrete nonlinear equations with non-Gaussian stochastic input, where the statistical properties of stochastic input are unknown. By using Parzen windowing with Gaussian kernel to estimate the probability densities of errors, recursive algorithms are then proposed to design the controller such that the tracking error can be minimized. The performance of the error-entropy minimization is compared with the mean-square-error minimization in the simulation results.

Original language	English
Pages (from-to)	10407-10412
Number of pages	6
Journal	IFAC-PapersOnLine
Volume	50
Issue number	1
DOIs	https://doi.org/10.1016/j.ifacol.2017.08.1720
State	Published - Jul 2017
Externally published	Yes

Funding

Indus∗∗tSrtieaste, NKoerythLeaabsoterarntorUynoivfeSrsyintyth,eStihceanlyAauntgom11a0t8io1n9,foCrhiPnraoc(ees-smail: IndustSrtieaste, NKoerythLeaabsoterarntorUynoivfeSrsyintyth,eStihceanlyAauntgom11a0t8io1n9,foCrhiPnraoc(ees-smail: ∗∗Institute of CompulitueyruSnclioenngcbeusa, [email protected])ersity, Anhui, China ∗∗∗∗∗Institute of CompulitueyruSnclioenngcbeusa,[email protected])ersity, Anhui, China ∗∗∗ISncsiteitnuctee aonfdCTomecphuntoelrogSycioenncAesir,cAranfthuCioUnntriovlerLsaibtyo,raAtonrhyu,i,BCeihhiannag ∗∗∗ISncsiteitnucte aonfdCTomecphuntoelrogSycioenncAesir,cAranfthuCioUnntriovlerLsaibtyo,raAtonrhyu,i,BCeihhiannag ∗∗∗UScniievnecresitayn,dBTeeijcihnngo1lo0g0y19o1n, ACihrcinraaft(eC-monatirlo:[email protected],uB.cenih)ang ∗US∗cn∗i∗ievnecresitayn,dBTeeijcihnngo1lo0g0y19o1n, ACihrcinraaft(eC-monatirlo:[email protected],uB.cenih)ang UnivPerasciitfyic, BNeoirjitnhwg e1s0t0N19a1ti,oCnahlinLaab(oer-amtoarily:,[email protected])d ∗U∗n∗∗ivPerasciitfyic, BNeoirjitnhwg e1s0t0N19a1ti,oCnahlinLaab(oer-amtoarily:,[email protected])d ∗∗∗∗∗∗∗∗RicPhalacnifdic, WNoArt9h9w3e5s2t NUaStAion(ae-lmLaaiblo:rhaotonrgy.w, [email protected])lvd RicPhalacnifdic, WNoArt9h9w3e5s2t NUaStAion(ae-lmLaaiblo:rhaotonrgy.w, [email protected])lvd Richland, WA 99352 USA (e-mail: [email protected]) Richland, WA 99352 USA (e-mail: [email protected]) Abstract: This paper presents an error-entropy minimization tracking control algorithm for a Abstract: This paper presents an error-entropy minimization tracking control algorithm for a ncloanslsinoefadryneqaumaitciosntoschwaistthicnsoyns-tGemaus.ssTiahne ssytsotcehmasitsicreipnrpeuset,ntwedhebrye athseetsotfattiimstiec-avlarpyrionpgedrtisiecsretoef nloanslsinoefadryneqaumaitciosntoschwaistthicnsoyns-tGemaus.ssTiahne ssytsotcehmasitsicreipnrpeuset,ntwedhebrye athseetsotfattiimstiec-avlarpyrionpgedrtisiecsretoef sntoonclhinaesatirc einqpuuattioanrse uwnitkhnonwonn.-GBayusussiianng sPtaorczheanstwicinidnopwutin, gwwheitrhe Gthaeussstiaatnistkiecranlepl rtoopesrttiimesatoef ntoonclhinaesatirc einqpuuattioanrse uwnitkhnonwonn.-GBayusussiianng sPtaorczheanstwicinidnopwutin, gwwheitrhe Gthaeusstiaatnistkiecranlepl rtoopesrttiimesatoef cthonetrporlolebrasbuilcihtythdaetntshiteietsraocfkinergroerrsr,orrceacnurbsievemianligmorizitehdm. Ts haerepetrhfoernmapnrocep osfetdhetoerrdoers-iegnntrotphye chonetrporlolebrasbuilcihtythdaetntshiteietsraocfkinergroerrsr,orrceacnurbsievemianligmorizitehdm. Ts haerepetrhfoernmapnrocep osfetdhetoerrdoers-iegnntrotphye mcointirmolilzeartisounchistchoamt pthaeretdrawckitihngtheerrmorecaann-sbqueamrei-neirmroizremd.inTihmeizpaetriofonrminanthce soifmtuhleateirornorr-esnutrltosp.y mointirmolilzeartisounchistchoamt pthaeretdrawckitihngtheerrmorecaann-sbqueamrei-neirmroizremd.inTihmeizpaetriofonrminanthce soifmtuhleateirornorr-esnutrltosp.y © 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Minimum error entropy, information potential, non-Gaussian variables, probability Keywords: Minimum error entropy, information potential, non-Gaussian variables, probability dKeenyswitoyrdfus:nMctiionnim, sutmocherarsotricesnytsrtoepmy,s.information potential, non-Gaussian variables, probability dKeenyswitoyrdfus:nMctiionnim, sutmocherarsotricesnytsrtoepmy,s.information potential, non-Gaussian variables, probability density function, stochastic systems. density function, stochastic systems. 1. INTRODUCTION 1. INTRODUCTION 1. 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Hdioswtreivbeurt,iomno(sstereeaAl-tlhifaenssy[s1t9e7m1s])a. re governed by nonlinear However, most real-life systems are governed by nonlinear mGaoudseslisananddistmriobsuttesdto. cThahsetriecfonreo,isesstoachreastfaicr dfrisotmribbuetiinong Gaoudseslisananddistmriobsuttesdto. cThahsetriecfonreo,isesstoachreastfaicr dfrisotmribbuetiinong creofnetrreonlce(sseteherWeiann)gfor[2n0o0n0-]G, aYuusesiaannsdtoWchaanstgic [s2y0s0t3em] ahnads ceofnetrreonlce(sseteherWeiann)gfor[2n0o0n0-]G, aYuusesiaannsdtoWchaanstgic [s2y0s0t3em] ahnads rbefeenresntcuedsiethdeerxeitne)nsfiovrenlyonin-Greacuesnstiayneastroscihnarsetsicposynssteetmo hthaes beefeenresntcuedsiethdeerxeitne)nsfiovrenlyonin-Greacuesnstiayneastroscihnarsetsicposynssteetmo hthaes binecerneassteuddieredqeuxirteemnseivnetslyoinf rmecaennyt yperaarcstiicnalressypsotnemsest.oTthhe bnecerneassteuddieredqeuxirteemnseivnetslyoinf rmecaennyt yperaarcstiicnalressypsotnemsest.oTthhee pdreismiganrycopnutrrpolosienpouf tstsoucchhastthicatditshtreibpurtoiobnabciolintytrodlenissittyo deismiganrycopnutrrpolosienpouf tstsoucchhastthicatditshtreibpurtoiobnabciolintytrodlenissittyo dfuensicgtnionco(nPtDroFl) ionfpcuotrrseuspchontdhinagt rtahnedopmrobvaarbiialbitlye idsemnsaidtye fuensicgtnionco(nPtDroFl) ionfpcuotrrseuspchontdhinagt rtahnedopmrobvaarbiialbitlye idsemnsaidtye function (PDF) of corresponding random variable is made ⋆function (PDF) of corresponding random variable is made ⋆ This work was supported in part by the National Natural Science ⋆ This work was supported in part by the National Natural Science F⋆oTunhdisatwioonrkowfaCshsiunpapourntdederinGpraanrt b6y13t3h3e0N07a,ti6o1n6a2l1N0a0t4u,r6a1l5S7c3ie0n2c2e, FoTunhdisatwioonrkowf aCshsiunpapourntdederinGpraanrtt b6y13t3h3e0N07a,ti6o1n6a2l1N0a0t4u,r6a1l 5S7c3ie0n2c2e, FhoeunCdhaitnieosne oNfaCtiohninaal Puonsdte-droGctroarntSc6ie1n3c3e30F0o7u,n6d1a6t2io1n00u4n,d6e1r5G73ra0n2t2s, th0e15CMh5in7e1s3e22NaatnidonCalCPSoIsot-fdtohcetoPraSccifiiecnNceorFtohuwnedsattNioantiuonndaelrLGabraonrats-th0e15CMh5in7e1s3e22NaatnidonCalCPSoIsot-fdtohcetoPraSccifiiecnNceorFtohuwnedsattNioantiuonndaelrLGabraonrats-ttoo0rr1yy5..M571322 and CCSI of the Pacific Northwest National Laboratory. Copyright © 2017 IFAC 10894 2405-8963 © 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. CPeer review under responsibility of International Federation of Automatic Control.opyright © 2017 IFAC 10894 Copyright © 2017 IFAC 10894 10.1016/j.ifacol.2017.08.1720

Keywords

Minimum error entropy
information potential
non-Gaussian variables
probability density function
stochastic systems

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10.1016/j.ifacol.2017.08.1720

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@article{d731b3341985470383d913e4c9e3259e,

title = "An Error-Entropy Minimization Algorithm for Tracking Control of Nonlinear Stochastic Systems with Non-Gaussian Variables",

abstract = "This paper presents an error-entropy minimization tracking control algorithm for a class of dynamic stochastic systems. The system is represented by a set of time-varying discrete nonlinear equations with non-Gaussian stochastic input, where the statistical properties of stochastic input are unknown. By using Parzen windowing with Gaussian kernel to estimate the probability densities of errors, recursive algorithms are then proposed to design the controller such that the tracking error can be minimized. The performance of the error-entropy minimization is compared with the mean-square-error minimization in the simulation results.",

keywords = "Minimum error entropy, information potential, non-Gaussian variables, probability density function, stochastic systems",

author = "Yunlong Liu and Aiping Wang and Lei Guo and Hong Wang",

note = "Publisher Copyright: {\textcopyright} 2017",

year = "2017",

month = jul,

doi = "10.1016/j.ifacol.2017.08.1720",

language = "English",

volume = "50",

pages = "10407--10412",

journal = "IFAC-PapersOnLine",

issn = "1474-6670",

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T1 - An Error-Entropy Minimization Algorithm for Tracking Control of Nonlinear Stochastic Systems with Non-Gaussian Variables

AU - Liu, Yunlong

AU - Wang, Aiping

AU - Guo, Lei

AU - Wang, Hong

PY - 2017/7

Y1 - 2017/7

N2 - This paper presents an error-entropy minimization tracking control algorithm for a class of dynamic stochastic systems. The system is represented by a set of time-varying discrete nonlinear equations with non-Gaussian stochastic input, where the statistical properties of stochastic input are unknown. By using Parzen windowing with Gaussian kernel to estimate the probability densities of errors, recursive algorithms are then proposed to design the controller such that the tracking error can be minimized. The performance of the error-entropy minimization is compared with the mean-square-error minimization in the simulation results.

AB - This paper presents an error-entropy minimization tracking control algorithm for a class of dynamic stochastic systems. The system is represented by a set of time-varying discrete nonlinear equations with non-Gaussian stochastic input, where the statistical properties of stochastic input are unknown. By using Parzen windowing with Gaussian kernel to estimate the probability densities of errors, recursive algorithms are then proposed to design the controller such that the tracking error can be minimized. The performance of the error-entropy minimization is compared with the mean-square-error minimization in the simulation results.

KW - Minimum error entropy

KW - information potential

KW - non-Gaussian variables

KW - probability density function

KW - stochastic systems

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DO - 10.1016/j.ifacol.2017.08.1720

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AN - SCOPUS:85031794255

SN - 1474-6670

VL - 50

SP - 10407

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JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

IS - 1

ER -

An Error-Entropy Minimization Algorithm for Tracking Control of Nonlinear Stochastic Systems with Non-Gaussian Variables

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