If you are aiming to control heat levels then you will have a very hard time to do it, each of these induction rings is a complete feedback and safety system.
They each have a microcontroller and possibly multiplexed inputs and outputs.
Basically you want to "Hack" an induction hot top, can I suggest you Google.
hacking inductive cookers
It is not at this point will an Arduino do it, its can it be done.
You need to consult the people who now about the control systems of induction cookers.
PS. I have repaired some of these units but have no understanding of the intricacies of controlling them.