  This paper addresses the problem of risk-aware fixed-time stabilization of a
class of uncertain, output-feedback nonlinear systems modeled via stochastic
differential equations. First, novel classes of certificate functions, namely
risk-aware fixed-time- and risk-aware path-integral-control Lyapunov functions,
are introduced. Then, it is shown how the use of either for control design
certifies that a system is both stable in probability and probabilistically
fixed-time convergent (for a given probability) to a goal set. That is, the
system trajectories probabilistically reach the set within a finite time,
independent of the initial condition, despite the additional presence of
measurement noise. These methods represent an improvement over the
state-of-the-art in stochastic fixed-time stabilization, which presently offers
bounds on the settling-time function in expectation only. The theoretical
results are verified by an empirical study on an illustrative, stochastic,
nonlinear system and the proposed controllers are evaluated against an existing
method. Finally, the methods are demonstrated via a simulated fixed-wing aerial
robot on a reach-avoid scenario to highlight their ability to certify the
probability that a system safely reaches its goal.
