Optimistic robust linear quadratic dual control
Proceedings of the 2nd Conference on Learning for Dynamics and Control, PMLR 120:550-560, 2020.
Recent work by Mania et al. has proved that certainty equivalent control achieves optimal regret for linear systems and quadratic costs. However, when parameter uncertainty is large, certainty equivalence cannot be relied upon to stabilize the true, unknown system. In this paper, we present a dual control strategy that attempts to combine the performance of certainty equivalence, with the practical utility of robustness. The formulation preserves structure in the representation of parametric uncertainty, which allows the controller to target reduction of uncertainty in the parameters that ‘matter most’ for the control task, while robustly stabilizing the uncertain system. Control synthesis proceeds via convex optimization, and the method is illustrated on a numerical example.