We consider feedback control systems where sensor readings may be compromised by a malicious attacker intending on causing damage to the system. We study this problem at the supervisory layer of the control system, using discrete event systems techniques. We assume that the attacker can edit the outputs from the sensors of the system before they reach the supervisory controller. In this context, we formulate the problem of synthesizing a supervisor that is robust against the class of edit attacks on the sensor readings and present a solution methodology for this problem. This methodology blends techniques from games on automata with imperfect information with results from supervisory control theory of partially-observed discrete event systems. Necessary and sufficient conditions are provided for the investigated problem.