Regional Controllability of the Position and Fractional Speed of Linear Hyperbolic Systems

This research focuses on exploring the regional controllability of position and fractional velocity within internally controlled hyperbolic systems. To achieve this, we leverage the Hilbert Uniqueness Method (HUM), which enables us to identify a control strategy that guides the attained position (resp. fractional speed) to the desired position within a specified subregion \(\omega \) $\omega$ of the domain \(\Omega \) $\mathrm{\Omega }$ (resp. the speed within the evolution domain \(\Omega \) $\mathrm{\Omega }$ ) by time T. Consequently, we employ a numerical technique to derive an explicit expression for the optimal control. Furthermore, we conduct numerical simulations to validate the obtained results.