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The objective of this work is to provide a theoretical formulation for optimal switching of a moving (or scanning) actuator for distributed parameter systems. The proposed hybrid controller switches both the location and control signal of the plant at the beginning of a time interval and remains unchanged over the duration of the time interval. This is repeated for different time intervals. The method employed is based on LQR optimal control. First, a set of admissible locations for which the moving actuator can reside at throughout the duration of a given time interval is considered. Guiding the moving actuator at these a priori selected positions at different time intervals is made possible by solving a double optimization problem. Further, an optimal set of admissible locations at which the moving actuator can reside at throughout the duration of a given time interval is chosen. A numerical example with simulation results is presented.