In [1], the authors show that using a mobil cuople of Actuator/Sensor (or a network of mobil Actuators/Sensors) improves the settling time of the diffusion equation.

[1] Demetriou, M. A. (2010). Guidance of mobile actuator-plus-sensor networks for improved control and estimation of distributed parameter systems. IEEE Transactions on Automatic Control, 55(7), 1570-1584.