  We present safe control of partially-observed linear time-varying systems in
the presence of unknown and unpredictable process and measurement noise. We
introduce a control algorithm that minimizes dynamic regret, i.e., that
minimizes the suboptimality against an optimal clairvoyant controller that
knows the unpredictable future a priori. Specifically, our algorithm minimizes
the worst-case dynamic regret among all possible noise realizations given a
worst-case total noise magnitude. To this end, the control algorithm accounts
for three key challenges: safety constraints; partially-observed time-varying
systems; and unpredictable process and measurement noise. We are motivated by
the future of autonomy where robots will autonomously perform complex tasks
despite unknown and unpredictable disturbances leveraging their on-board
control and sensing capabilities. To synthesize our minimal-regret controller,
we formulate a constrained semi-definite program based on a System Level
Synthesis approach for partially-observed time-varying systems. We validate our
algorithm in simulated scenarios, including trajectory tracking scenarios of a
hovering quadrotor collecting GPS and IMU measurements. Our algorithm is
observed to have better performance than either or both the $\mathcal{H}_2$ and
$\mathcal{H}_\infty$ controllers, demonstrating a Best of Both Worlds
performance.
