Energy-based schemes for the guidance of mobile actuator/sensor pairs in the control of first order infinite dimensional systems

The paper is concerned with an alternative method in addressing the effects of spatiotemporally varying disturbances in controlling spatially distributed systems. Use of robust control schemes for controlling partial differential equations may not provide acceptable controller authority in handling “moving” disturbances. A way to handle such a case is to consider the use of mobile actuators. In this work, we consider a class of spatially distributed systems which employ a collocated actuator/sensor pair. By using the a priori defined structure of static output feedback, the problem then remains that of determining the spatial repositioning of the actuatro/sensor pair throughout the spatial domain. Using energy-based methods based on the state norm of the spatially distributed system, two guidance policies associated with two different actuator distribution functions are developed. Simulation results for a 1D diffusion equation with a “moving” disturbance are included to provide some insight on the effective handling of such moving disturbances via mobile actuator/sensor pairs.