  In time-critical systems, such as air traffic control systems, it is crucial
to design control policies that are robust to timing uncertainty. Recently, the
notion of Asynchronous Temporal Robustness (ATR) was proposed to capture the
robustness of a system trajectory against individual time shifts in its
sub-trajectories. In a multi-robot system, this may correspond to individual
robots being delayed or early. Control synthesis under ATR constraints is
challenging and has not yet been addressed. In this paper, we propose an
efficient control synthesis method under ATR constraints which are defined with
respect to simple safety or complex signal temporal logic specifications. Given
an ATR bound, we compute a sequence of control inputs so that the specification
is satisfied by the system as long as each sub-trajectory is shifted not more
than the ATR bound. We avoid combinatorially exploring all shifted
sub-trajectories by first identifying redundancy between them. We capture this
insight by the notion of instant-shift pair sets, and then propose an
optimization program that enforces the specification only over the
instant-shift pair sets. We show soundness and completeness of our method and
analyze its computational complexity. Finally, we present various illustrative
case studies.
