This　paper　designs　two　novel　event-triggered　control　(ETC)　schemes　based　on　the　critic　learning　technique　for　constrained　discrete-time　nonlinear　systems.　First,　starting　from　the　stability　of　the　constrained　system,　a　static　ETC　method　is　developed　to　reduce　the　computational　burden.　Then,　a　nonnegative　dynamic　variable　is　introduced　into　the　static　event-triggered　mechanism,　so　as　to　establish　the　dynamic　ETC　method,　which　further　improves　the　resource　utilization　rate　and　possesses　the　anti-interference　ability.　Moreover,　a　speedy　value　iteration　architecture　is　designed　to　obtain　an　initially　admissible　optimal　control　policy,　which　can　ensure　the　normal　execution　of　the　designed　ETC　methods.　Finally,　two　experimental　examples　are　provided　to　illustrate　the　effectiveness　and　superiority　of　the　developed　schemes.