This paper addresses the problem of controlling a system, subject to disturbances, to prevent exit from a safe region of the state space. Problems of this nature are encountered in many different contexts, for example in the control of tanks to avoid overflow and of operation of telecommunications systems to avoid the failing of a communications link. The proposed control methodology is based on solving a differential game, in which a feedback control is found that minimizes the disturbance energy to force the state out of the safe region. Such controls also have interpretations in terms of stochastic exit-time problems. We announce a new class of exit problems, including problems with high state dimension, for which the related game can be simply computed. The proposed solution technique involves the on-line solution of $N$ optimal control problems where, typically, $N$ is small. Accordingly, the computational effort is several times larger, but still of the same order of magnitude, as that involved in implementing a standard non-linear model predictive controller.