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

Safe Control of Partially-Observed Linear Time-Varying Systems with Minimal Worst-Case Dynamic Regret