  This paper tackles the problem of generating safe exit controllers for
continuous-time systems described by stochastic differential equations (SDEs).
The primary aim is to develop controllers that maximize the lower bounds of the
exit probability that the system escapes from a safe but uncomfortable set
within a specified time frame and guide it towards a comfortable set. The paper
considers two distinct cases: one in which the boundary of the safe set is a
subset of the boundary of the uncomfortable set, and the other where the
boundaries of the two sets do not intersect. To begin, we present a sufficient
condition for establishing lower bounds on the exit probability in the first
case. This condition serves as a guideline for constructing an online linear
programming problem. The linear programming problem is designed to implicitly
synthesize an optimal exit controller that maximizes the lower bounds of the
exit probability. The method employed in the first case is then extended to the
second one. Finally, we demonstrate the effectiveness of the proposed
approaches on one example.
