In this paper, a resilient distributed control scheme against covert attacks for multi-agent networked systems subject to input and state constraints is developed. The idea consists in a clever deployment of predictive arguments with a twofold aim: detection of malicious agent behaviors affecting the normal system operations and consequent specific control actions implementation to mitigate as much as possible undesirable knock-on effects resulting from adversary actions. Specifically, the multi-agent system is organized in terms of a grid topology and set-theoretic receding horizon control ideas are exploited to develop a distributed algorithm capable to recognize the attacked agent. In essence, the resulting solution relies on the combined use of predictive control and set-invariance ideas that are exploited to generate redundant control sequences randomly selected on the actuator side such that the malicious agent is never aware about the effective control action indeed exploited. As a consequence, countermeasures on the sensor-to-controller channel could lead to significantly erroneous data not complying with the expected evolution of the system modeling. Finally, numerical simulations are carried out to show benefits and effectiveness of the proposed approach.