Membership　function　identification　is　the　basis　for　solving　the　fuzzy　control　problems.　In　order　to　complete　the　fuzzification　process　and　reflect　the　dynamic　quality　of　the　nonlinear　systems　accurately,　this　paper　constructs　a　kernel　function-based　nonlinear　system　by　introducing　the　multi-model　control　strategy,　and　it　has　a　good　performance　in　fitting　nonlinear　systems.　Then　we　focus　on　the　parameter　estimation　problem　of　the　nonlinear　systems　based　on　the　kernel　functions.　To　overcome　the　difficulty　due　to　the　highly　nonlinear　relations　between　the　parameters　and　the　model　output,　we　transform　the　original　optimization　problem　into　a　quadratic　and　a　nonlinear　optimization　problems　by　decomposing　the　complex　identification　model　into　two　sub-models.　Based　on　the　hierarchical　identification　principle　and　the　multi-innovation　theory,　two　recursive　identification　algorithms　are　proposed　for　the　nonlinear　systems.　Considering　the　difficulty　to　determine　the　step　sizes,　we　derive　the　optimal　step　sizes　by　the　one-dimensional　search　method.　The　effectiveness　of　the　proposed　algorithms　are　tested　by　a　numerical　example.　The　simulation　results　show　that　the　proposed　parameter　identification　methods　can　identify　the　nonlinear　systems　effectively.　©　2021,　The　Author(s),　under　exclusive　licence　to　Springer　Nature　B.V.