In　this　article,　to　solve　the　optimal　tracking　control　problem　(OTCP)　for　discrete-time　(DT)　nonlinear　systems,　general　value　iteration　(GVI)　scheme　and　online　value　iteration　(VI)　algorithms　with　novel　value　function　are　discussed.　First,　the　disadvantage　of　the　traditional　value　function　for　the　OTCP　is　presented　and　the　novel　value　function　is　introduced.　Second,　we　analyze　the　monotonicity　and　convergence　of　GVI　and　establish　the　admissibility　condition　of　GVI　to　evaluate　the　admissibility　of　the　current　iterative　control.　Note　that　a　novel　approach　is　introduced　to　analyze　the　admissibility.　Third,　based　on　the　attraction　domain,　improved　control　policies　with　online　VI　can　be　obtained　by　judging　the　location　of　the　current　tracking　error　and　reference　point.　Finally,　the　stability　of　the　online　VI-based　control　system　is　guaranteed.　Besides,　we　provide　two　simulation　examples　to　show　the　performance　of　the　proposed　methods.