Adissipative-basedadaptiveneuralcontrolschemewasdevelopedforaclassofnonlinearuncertainsystemswithunknownnonlinearitiesthatmightnotbelinearlyparameterized.Themajoradvantageofthepresentworkwastorelaxtherequirementofmatchingcondition,I.e.,theunknownnonlinearitiesappearonthesameequationasthecontrolinputinastate-spacerepresentation,whichwasrequiredinmostoftheavailableneuralnetworkcontrollers.Bysynthesizingastate-feedbackneuralcontrollertonaketheclosed-loopsystemdissipativewithrespecttoaquadraticsupplyrate,thedevelopedcontrolschemeguaranteesthattheL2-gainofcontrolledsystemwaslessthanorequaltoaprescribedlevel.Andthen,itisshownthattheoutputtrackingerrorisuniformlyultimatebounded.Thedesignschemeisillustratedusinganumericalsimulation.