This　article　proposes　two　adaptive　asymptotic　tracking　control　schemes　for　a　class　of　interconnected　systems　with　unmodeled　dynamics　and　prescribed　performance.　By　applying　an　inherent　property　of　radial　basis　function　(RBF)　neural　networks　(NNs),　the　design　difficulties　aroused　from　the　unknown　interactions　among　subsystems　and　unmodeled　dynamics　are　overcome.　Then,　in　order　to　ensure　that　the　tracking　errors　can　be　suppressed　in　the　specified　range,　the　constrained　control　problem　is　transformed　into　the　stabilization　problem　by　using　an　auxiliary　function.　Based　on　the　adaptive　backstepping　method,　a　time-triggered　controller　is　constructed.　It　is　proven　that　under　the　framework　of　Barbalat＇s　lemma,　all　the　variables　in　the　closed-loop　system　are　bounded　and　the　tracking　errors　are　further　ensured　to　converge　to　zero　asymptotically.　Furthermore,　the　event-triggered　strategy　with　a　variable　threshold　is　adopted　to　make　more　precise　control　such　that　the　better　system　performance　can　be　obtained,　which　reduces　the　system　communication　burden　under　the　condition　of　limited　communication　resources.　Finally,　an　illustrative　example　is　provided　to　demonstrate　the　effectiveness　of　the　proposed　control　scheme.