In　this　thesis,　we　construct　improved　value　iteration　(VI)　and　online　VI　structures,　in　a　bid　to　tackle　the　optimal　tracking　control　problem　for　discrete-time　nonlinear　systems.　Note　that　asymmetric　control　restraints　and　the　discount　factor　are　considered.　First,　related　properties　are　discussed　for　novel　VI,　involving　the　monotonicity　of　the　iterative　cost　function　sequence　and　the　admissibility　of　the　iterative　tracking　control　policy.　Second,　the　stability　condition　for　the　discount　factor　is　provided　to　ensure　the　stability　of　all　iterative　tracking　control　policies,　which　are　created　by　stabilizing　VI.　Third,　by　combining　novel　VI　and　stabilizing　VI,　an　improved　VI　algorithm　is　developed,　where　iterative　cost　function　sequences　are　monotonically　nondecreasing　and　nonincreasing　during　novel　VI　and　stabilizing　VI　stages,　respectively.　Fourth,　with　the　appropriate　discount　factor,　an　online　VI　algorithm　is　proposed　by　integrating　the　attraction　domain　with　improved　VI.　Also,　under　the　online　VI　structure,　the　asymptotic　stability　proof　is　performed　for　the　tracking　error　system.　Finally,　regarding　theoretical　contributions　are　illustrated　by　a　simulation　case.