  We present an optimisation-based method for synthesising a dynamic regret
optimal controller for linear systems with potentially adversarial disturbances
and known or adversarial initial conditions. The dynamic regret is defined as
the difference between the true incurred cost of the system and the cost which
could have optimally been achieved under any input sequence having full
knowledge of all future disturbances for a given disturbance energy. This
problem formulation can be seen as an alternative to classical $\mathcal{H}_2$-
or $\mathcal{H}_\infty$-control. The proposed controller synthesis is based on
the system level parametrisation, which allows reformulating the dynamic regret
problem as a semi-definite problem. This yields a new framework that allows to
consider structured dynamic regret problems, which have not yet been considered
in the literature. For known pointwise ellipsoidal bounds on the disturbance,
we show that the dynamic regret bound can be improved compared to using only a
bounded energy assumption and that the optimal dynamic regret bound differs by
at most a factor of $\frac{2}{\pi}$ from the computed solution. Furthermore,
the proposed framework allows guaranteeing state and input constraint
satisfaction.
