Constrained Optimization

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1、IntroductiontoConstrainedOptimizationIntroductiontoConstrainedOptimizationZhongyuZhongyuTieTieSchoolofInformationScienceandEngggineeringOutline¾Part0Preface¾PartIIntroduction¾partIIMethods¾partIIIExperimentalresults¾partⅣConclusionandfutureworkPrefaceWhatisoptimization?Inmathema

2、ticsandcomputationalscience,mathematicaloptimization(alternatively,optimizationormathematicalprogramming)referstotheseltilectionofabtbesteltlementfromsomesetofavailblilablealternatives.Whatisoptimizationmethod?Optimizationmethod(alsocalledoperationsresearchmethods)mainlyusesmath

3、ematicalmethodstofindoptimalwaysandsolutionstosystems,providingscientificbasisfordecision-makers.Whatisaoptimizationproblem?Itusuallyconsistsofaobjectivefunction,somedecisionvariablesandconstraints.Bytheway,theoptimizationmethodistofindtheoptimaldiidecisionvaribliablesfortheobjt

4、ibjectiveftfunctiionundertheconstittraints.PrefaceThedifferencesbetweenmodelingandoptimization,andcontrolandoptimizationModelingistofindamathematicalmodeltodescribetherelationshipbetweentheinputsandoutputs.Itisusuallycomposedoftheselectionofamodelstructureandanestimationofthemod

5、el’sparameters.Acontrolsystemisaninterconnectionofcomponentsformingasystemconfigurationthatwillprovideadesiredsystemresponse.Optimizationisamethod(technique)tofindtheoptimal(best)modelorcontrollerforthesystem.PrefaceTransformingarealworldproblemintoanoptimizationproblemDesigning

6、acontrollertomeettherequirements•Stability•DynamicperformanceRisetime,DDlelaytime,PPktieaktime,SSttliettlingtime,Overshoot,OscillationtimesPrefaceTypesofcontroller①PIDcontrollerPIDcontroller②Fuzzycontroller③NlNeuralnetworkkcontrollller④Statefeedbackcontroller⑤Outputfeedbackcontr

7、ollerMethodsforstability①Routh-Hurwitzcriterion②Nyquistcriterion③Rootlocusplot④Bodediagram⑤Lyapunov’sstabilitycriterionPrefaceTheremethodsarejustanalyticalapproaches,becausetheconceptofstabilityisnotclear.Howtoascertainorquantifythestability?Obviously,iftheerrorbetweenthedesired

8、outputyandoutputyis0,rthesystemisstable.Ontheba