Regional fractional zone moving control for linear hyperbolic systems: Numerical approximation and optimization

Abstract

Summary This work focuses on the exact fractional controllability of linear hyperbolic systems over a finite time interval. The control is applied to the internal moving zone of a predefined actuator location in the spatial domain of the system. We use the Hilbert uniqueness method (HUM) to characterize the minimum‐energy control that enables us to achieve the desired fractional state at time . We therefore consider a numerical approach that allows us to determine the explicit formula for optimal control. We also verify the results' applicability using computer simulations for the one‐dimensional wave equation with a moving zone actuator.