An optimization approach is proposed to derive non-linear model-based control laws for non-linear processes with actuator saturation non-linearities. The derived control laws induce a linear closed-loop process output response in the absence of input constraints (are input-output linearizing), are able to minimize the mismatch between the constrained and the linear unconstrained process output responses, and inherently include optimal directionality and windup compensators. Connections between the derived control laws and (a) already available, input-output linearizing, non-linear, control methods, (b) modified internal model control, and (c) model state feedback control, are established. The application and performance of the derived control laws are shown by examples.