In　this　article,　the　consensus　of　constrained　linear　heterogeneous　multiagent　systems　under　prediction　and　optimization　is　investigated.　By　optimizing　the　consensus　problems　constrained　to　state　equations　and　general　linear　constraints,　two　types　of　distributed　analytical　model　predictive　controllers　are　proposed.　Furthermore,　stability　conditions　for　the　two　types　of　controllers　are　derived,　in　which　a　relationship　between　the　communication　topology　and　dynamics　of　heterogeneous　agents　is　clarified.　Simulation　examples　of　networked　heterogeneous　agents　illustrate　the　convergence　and　validity　of　the　proposed　controllers.