In this letter, a resilient control strategy against replay attacks is developed for discrete-time linear systems subject to state and input constraints, bounded disturbances, and measurement noises. In particular operating scenarios, where adversaries act on the communication network by maliciously repeating data transmitted from the sensor to the controller, are investigated. The idea is to customize basic model predictive control schemes for detection attack and resilient control action purposes by exploiting set-theoretic and feasibility arguments proper of the receding control horizon philosophy.