This　paper　proposes　an　event-based　near-optimal　control　algorithm　for　nonaffine　discrete-time　systems　with　constrained　inputs.　The　method　is　derived　from　the　dual　heuristic　dynamic　programming　(DHP)　technique.　The　challenge　caused　by　saturating　actuators　is　overcome　by　using　a　nonquadratic　performance　index.　Then,　the　event-based　control　technique　is　used　to　decrease　the　amount　of　computation.　Meanwhile,　the　stability　analysis　is　provided.　It　illustrates　that　the　proposed　event-based　method　can　asymptotically　stabilize　the　nonaffine　systems　by　using　the　Lyapunov　method.　Furthermore,　the　stability　conditions　and　the　design　process　of　the　event-based　controller　are　established.　The　event-based　DHP　algorithm　is　implemented　by　constructing　three　neural　networks,　namely,　the　model　network,　the　critic　network,　and　the　action　network.　Finally,　simulation　studies　are　conducted　to　demonstrate　the　applicability　and　the　performance　of　the　proposed　method.　(C)　2020　Elsevier　Inc.　All　rights　reserved.