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In this link, two methods have been referred for linearization.

1- offline linearization

2- online linearization

However, I do not understand what is the role of "successive linearization" in the online method. What is the difference between successive and typical linearization?

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In the section "Implement Adaptive MPC Control of CSTR Plant in Simulink (R)":

The model includes three parts:

[...]

  1. The "Successive Linearizer" block [...] that [...] provides the linear plant model to the "Adaptive MPC Controller" block at each control interval.

If you look closely, they don't make a difference between typical and successive linearization, but call successive linearization and online estimation the two typical forms of online linearization. Read the second section, "About Adaptive Model Predictive Control" again, it is actually all explained there.

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