This　article　aims　to　design　a　model-free　adaptive　tracking　controller　for　discrete-time　nonlinear　systems　with　unknown　dynamics　and　asymmetric　control　constraints.　First,　a　new　Q-function　structure　is　designed　by　introducing　the　control　input　into　the　tracking　error　of　the　next　moment,　in　order　to　eliminate　the　final　tracking　error,　avoid　the　steady　control,　and　ignore　the　discount　factor.　Second,　via　system　transformation,　a　general　performance　index　is　developed　to　overcome　the　challenge　caused　by　asymmetric　constraints　of　implicit　control　inputs.　By　this　operation,　the　constrained　tracking　problem　is　converted　to　an　unconstrained　optimal　tracking　problem　without　the　traditional　nonquadratic　performance　function　that　is　only　applicable　to　explicit　control　inputs.　Then,　a　value-iteration-based　Q-learning　(VIQL)　algorithm　is　derived　to　seek　the　optimal　Q-function　and　the　optimal　control　policy　by　using　offline　data　rather　than　the　mathematical　model.　Next,　the　convergence,　monotonicity,　and　stability　properties　of　VIQL　are　investigated　to　demonstrate　that　the　iterative　Q-function　sequence　can　converge　to　the　optimal　Q-function　under　ideal　conditions.　To　realize　the　VIQL　algorithm,　the　critic　neural　network　is　employed　to　approximate　the　Q-function.　Finally,　simulation　results　and　comparative　experiments　are　conducted　to　demonstrate　the　validity　and　effectiveness　of　the　present　VIQL　scheme.　©　2024　John　Wiley　&　Sons　Ltd.