Page 399 - konishipaper

LookUpTable"inSimulink.ThebreakpointvaluesofP(v) aregivenby
り [-5，-4，-3，-2，-1，0，1，2，3，4，5] P(り [0.054217，0.12139，0.24345，0.39352，
0.1703，0.27545，0.292，0.1259， 0.25023，0.24345，0.021837]
where we select "cubic spline" as an interpolation method， and "linear" as an extrapolation method.Fig.4 shows the multimodalobjectivefunctionP(り.Figs.5and6showsthe convergenceprocesoftheobjectivefunctionandthedecision variable.Theinitialguesofthedecisionvariableisselected asv(O) 4.Theproposedsolverco即 ergestotheglobal mlmmum.
40 60 80 100 stcp
Fig.7. Convergencepropertyofobjectivefunctioninnoisycase.(solidline: objectivefunction，dotedline:objectivefunctionwithnoise).
Fig.4. MultimodalobjectivefunctionP(v). -0.1
Fig.8. Convergenceprop巴rtyofdecisionvariableinnoisycase.
IY. SIMULATIONRESULTSOFCAMMODEL A. Coupling Model 01 Two Cel ls
Kai proposed the synchronization model of C A M cel ls usingtheBZoscilatorsystem[14].Thismodelincludesthe fedbackcouplingsinωandx.Consideringthetransportof carbohydratesthroughvascularbundles，weproposedanother couplingmodel[10，] [15]:
X1=hUh，L1，T)+91(CextQ(t)-W1) +921L1(t)+931
X1=[W1 X1 Y1 Zl]T 931=[ED1(ωl(t-TL)一 切2(t-TL) 0 0 O]T X2=ん(ぬ，LぁT)+912(CextQ(t)一 切2)
-0.15
20
100
step
Fig.5. Convergencepropertyofobjectivefunctioninnoisefrecase.
-2
20 40 60 80 100 51ep
Fig.6. Convergenc巴 propertyofdecisionvariableinnoisefrecase.
Inreal-timeoptimizationusingmeasurementdata，anob- jectivefunctionisdisturbedbymeasurementnoises.Toinves- tigatetherobustnesoftheproposedoptimizationmethod，we adtheGausiannoiseN(O，0.052)totheobjectivefunction P(v) for each time. Under the same condition as in noise frecase，theproposedoptimizercanconvergetotheglobal minimumshowninFigs.7and8.
+922LO(t)+932
932= [ED2(ω2(t-TL)一 切 l(t-TL) 0 0 O]T
whereTL isatransportdelay，D1'D2 arethecoupling strengths，theparametersoftwocelsaresame，andtheinitial conditionsaredi百erent.
Undertheconstanttemperatureandthepulsedlighting， weperformthenumericalsimulationsforthretypesofthe coupling strengths: D 1 = D 2 = 0， D 1 = D 2 = 0.05， D 1 = -D2 = 0.05
Fig.9showstheresponsesofJco2 foreachcelandfor thretypesofthecouplingstrengths.Theresponsesarenot a百'ectedbythecouplingstrengths.
Using(4)，wecalculatethewholeCO2uptakewhenα1= Lα2= 0.8，L1 = 0，L2 = 0.2.Fig.lOshowsthewholeCO2 uptakeforthretypesofthecouplingstrengths.
X 2 = [ 7.均 Z 2 U 2 Z 2 l T
-1
-2 -3
40 60 80 100 51e，!