In　this　paper,　a　direct　current　model　predictive　control　(MPC)　strategy　is　adopted　to　address　the　regulation　of　output　voltage　for　the　interleaved　boost　converter.　The　control　strategy　combines　observer　based　adaptive　laws　with　direct　current　predictive　control　to　yield　an　adaptive　and　robust　controller.　The　adaptive　laws　are　designed　for　estimating　unknown　parameters　using　Lyapunov　stability　theory　and　updates　the　control　law　in　real　time.　To　demonstrate　the　effectiveness　of　the　proposed　control　strategy,　simulation　is　implemented　under　the　variation　of　input　voltage,　load　resistance　and　output　voltage　reference.　©　2019　IEEE.