This paper studies attackers with control objectives and explicit detection constraints against cyber-physical systems. The cyber-physical system is equipped with a Kalman filter and an attack detector that uses the innovations process of the Kalman filter. The attacker performs an integrity attack on the actuators and sensors of the system with the aim of moving the system to a target state under the constraint that the probability of him or her being detected is equal to the false alarm probability of the attack detector. We formulate and solve a constrained optimization problem that gives the optimal sequence of attacks and demonstrate our attack strategy in a numerical example.