On the links between real-time optimization, neighboring-extremal control, and self-optimizing control

In the context of process optimization, several techniques have been proposed in order to operate the plant near the economically optimal steady-state operating point. This paper discusses the links and differences between three of these techniques: (i) real-time optimization using the classical two-step approach, (ii) neighboring-extremal control with output feedback, and (iii) self-optimizing control using the null space method. It is argued that, under certain assumptions, the technique (ii) can be viewed as a first-order approximation of (i). Also, while (ii) and (iii) enforce similar optimal operations, their dynamic implementation and design features are very different.