Incremental rule-based control and learning

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1、Incrementalrule-basedcontrolandlearningD.LuzeauxEECSDepartmentUniversityofCaliforniaBerkeley,CA94720E-mail:luzeaux@robotics.berkeley.edu,luzeaux@etca.frAbstractThesecontrollawsarefurthermorerathereasytolearn:thisisCandide'sjobandwegiveinthepa-Autonomoussystemsarenowadaysachalle

2、ngeperthelearningmethodologyandshowhowCandidetomanyclassical"techniques:theyareeitherill-learnedtodriveacar.modeledorevolveinchangingenvironmentswhichperturbatethemdeeply.Itisnotpossibletoapplythewell-knownmathematicaltoolsandnewmethodshave2Incrementalrule-basedcontrollawstobe

3、foundtocontrolthem.Thesenewmethodsareusuallyknownasintelligentcontrolandincludeneu-Thesecontrollaws,whosemathematicalformula-ralnetworks,fuzzycontrol,qualitativecontrol,path-tionfollows,havebeenstudiedexperimentallyduringplanningmethodsandrule-basedreasoning.thelastyears[1,4,2]

4、;howevertheoreticalresultsareveryrecent[6,7].Inthispaperwerstintroduceincrementalrule-basedcontrollawsandthenwediscussalearningpro-2.1Theoreticalresultsgram,calledCandide,whichallowsalargeclassofsystemstosynthesizesuchcontrollawsinordertoper-formagiventask.Theincrementalrule-b

5、asedcontrollawshavethefollowingform:Ifoutputinthisrangethenincrease,decreaseorleavetheinput1IntroductionTheinputuattimekisrelatedtotheinputuatkk?1timek?1bytheequation:Whychooseincrementalrule-basedcontrollaws?8Theanswermayseemtorelymostlyonintuition0100u=u+u+
>kk?1kkk>>butrec

6、enttheoreticalresults[10,6]showtheideawas1112>u=u+u>kk?1kk>n?1n?1n?1n>>u=u+uknowledgeinmostcasesinadeclarativeform.Iftheykkk?1k>:nu=
havetoactonthesystem,theydonottrytosolvekacomplexe

7、quationandthenfeedthesolutiontothei0with:8i2f0;


;n?1g;8k2N;2f?1;0;1g;2system:theyusuallyincreasetheirpreviousactionorkk0f?m;


;mg,and
;
aretwopositiverealnum-decreaseitbysomeamountortheykeepitthesame.i0bers.ThecoecientsandwillbecalledsignskkTheincrementalrule-basedcont

8、rollawsarethefor-andthesetoftheirvaluesattimekisthesig