Sliding Mode Output Regulation for Linear $2 \times 2$ Hyperbolic System with Boundary Unmatched Disturbance

This paper investigates the sliding-mode output regulation problem of linear <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$2\times 2$</tex> hyperbolic PDE systems. The disturbances to which the system is subjected contains two types: modellable and unmatched disturbances. For modellable disturbance, the geometric design technique is employed to design compensator to compensate for the disturbance. For unmatched disturbance, the sliding-mode control technique is leveraged to constrain a particular system state to the sliding-mode surface, and thus eliminating the adverse impact of unmatched disturbances. We address the tracking control problem under these two types of disturbances on the basis of the existing work that only considers modellable disturbance. The comparative simulation verifies the effectiveness and advance of the proposed control scheme.