For　discrete-time　nonlinear　affine　systems　with　asymmetric　constraints,　an　adaptive　optimal　control　algorithm　is　established　in　this　paper,　which　is　implemented　through　dual　heuristic　dynamic　programming　(DHP).　A　novel　non-quadratic　performance　functional　is　presented　to　overcome　the　problem　caused　by　asymmetric　constrained　inputs.　Then,　under　the　adaptive　critic　framework,　three　neural　networks　are　constructed　for　implementing　the　DHP　algorithm,　which　are　designed　to　approximate　the　nonlinear　system,　the　costate　function,　and　the　control　law,　respectively.　Furthermore,　by　conducting　a　simulation　example　with　randomly　given　initial　state　vectors,　the　excellent　applicability　of　the　present　method　is　demonstrated.