Simplified controller design for distributed parameter systems using mobile actuator with augmented vehicle dynamics

A way to mitigate the effects of spatiotemporally varying disturbances in systems governed by partial differential equations is to employ actuating devices that are capable of moving throughout the spatial domain. In this work, the guidance of such a moving actuator, that is able to move throughout the spatial domain and dispense the control signal at any spatial location, is considered. By assuming a specific structure of the controller architecture, namely that of a collocated input-output in which the control signal is proportional to the state evaluated at the spatial location of the actuating device, the problem under consideration simplifies to that of obtaining the guidance of the moving actuator. By incorporating the dynamics of a moving vehicle, a Lyapunov stability argument is made in order to obtain the requisite control torque of the vehicle. Extensive numerical simulations for a diffusion equation are included to verify the effectiveness of a such a mobile actuator-sensor pair in suppressing the effects of spatially varying disturbances.