Optimistic robust linear quadratic dual control
This work addresses stabilization issues in control systems with high uncertainty, offering a practical solution for applications like robotics or autonomous vehicles, though it appears incremental as it builds on existing certainty equivalence methods.
The paper tackles the problem of stabilizing linear systems with large parameter uncertainty by proposing a dual control strategy that combines performance with robustness, allowing targeted uncertainty reduction while ensuring stability, and demonstrates it via convex optimization on a numerical example.
Recent work by Mania et al. has proved that certainty equivalent control achieves nearly optimal regret for linear systems with 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.