  As we move towards safety-critical cyber-physical systems that operate in
non-stationary and uncertain environments, it becomes crucial to close the gap
between classical optimal control algorithms and adaptive learning-based
methods. In this paper, we present an efficient optimization-based approach for
computing a finite-horizon robustly safe control policy that minimizes dynamic
regret, in the sense of the loss relative to the optimal sequence of control
actions selected in hindsight by a clairvoyant controller. By leveraging the
system level synthesis framework (SLS), our method extends recent results on
regret minimization for the linear quadratic regulator to optimal control
subject to hard safety constraints, and allows competing against a safety-aware
clairvoyant policy with minor modifications. Numerical experiments confirm
superior performance with respect to finite-horizon constrained $\mathcal{H}_2$
and $\mathcal{H}_\infty$ control laws when the disturbance realizations poorly
fit classical assumptions.
