简介：Biologicalelementsusuallyexerttheirfunctionsthroughinteractionswithotherstoformvarioustypesofbiologicalnetworks.Theabilityofcontrollingthedynamicsofbiologicalnetworksisofenormousbenefitstopharmaceuticalandmedicalindustryaswellasscientificresearch.Thoughtherearemanymathematicalmethodsforsteeringdynamicsystemstowardsdesiredstates,themethodsareusuallynotfeasibleforapplyingtocomplexbiologicalnetworks.Thedifficultiescomefromthelackofaccuratemodelthatcancapturethedynamicsofinteractionsbetweenbiologicalelementsandthefactthatmanymathematicalmethodsarecomputationallyintractableforlarge-scalenetworks.Recently,aconceptincontroltheory--controllability,hasbeenappliedtoinvestigatethedynamicsofcomplexnetworks.Inthisarticle,recentadvancesonthecontrollabilityofcomplexnetworksandapplicationstobiologicalnetworksarereviewed.Developingdynamicmodelsisthepriorconcernforanalyzingdynamicsofbiologicalnetworks.First,weintroduceawidelyuseddynamicmodelforinvestigatingcontrollabilityofcomplexnetworks.Thenrecentstudiesoftheoremsandalgorithmsforhavingcomplexbiologicalnetworkscontrollableingeneralorspecificapplicationscenariosarereviewed.Finally,applicationstorealbiologicalnetworksmanifestthatinvestigatingthecontrollabilityofbiologicalnetworkscanshedlightsonmanycriticalphysiologicalormedicalproblems,suchasrevealingbiologicalmechanismsandidentifyingdrugtargets,fromasystematicperspective.

简介：Thelinearcombinationofcertainpartitionofunity,subordinatetocertainopencoveringofacompactset,isprovedtobecapableofapproximatingtoacontinuousfunctionatarbitrarilyprecision.Byusingproperopencoveringandpartitionofunity,therobustnonlinearcontrollersandadaptivelawsaredesignedforaclassofnonlinearsystemswithuncertainties.Thestatesandparametersoftheclosed-loopsystemscanbestabilizedinthemeaningofUUB(uniformlyultimatelybounded)viatherobustnonlinearcontrollersandadaptivelaws.Finally,anexampleshowsthevalidityofmethodinthispaper.

简介：