A continuum of repetition takes place in reaction-convection processes described by first-order hyperbolic partial differential equations (PDEs). Especially, in cocurrent cases, they have finite impulse response (FIR) characteristics. Employing recently developed FIR property preserving finite difference scheme for cocurrent systems, a cocurrent first-order hyperbolic PDE system is recast as a repetitive process. Then a model predictive control scheme for repetitive processes is used for efficient control of cocurrent first-order hyperbolic PDE systems.