Robust control of PDEs with disturbances using mobile actuators constrained over time-varying reachability sets

We design a practical mobile actuator guidance policy for linear parabolic equations in 2D: the guidance is chosen so that ${\mathbb{H}^2}$-measure of uncertainty is minimized provided the system is subject to a distributed disturbance. We first present a guidance policy where the mobile actuator location to be selected will be fixed over a certain time interval of interest. Further we add extra complexity by taking into account the dynamics of the mobile actuator over the 2D domain of interest under reachability constraints. The proposed approach is illustrated through numerical studies.