I'm not familiar with induction cooktops, but this sounds suspiciously like an issue my son had on his glass-top stove last year.
For generations, burners were controlled by turning up or down the voltage being fed to the burners; the higher the voltage, the hotter the burner. On my son's and other newer cooktops, they've changed the way the temperature is regulated. Rather than allowing the voltage to go from 0V to, say, 220V, instead the voltage is fed to the burner at 220V directly. The term is Pulse Width Modulation, or PWM, where the temperature is regulated by turning the voltage on and off; the longer the time it's off, the cooler it is. Here's what it looks like in electrical terms.
[image|2836720]
The top image is what the signal looks like when the burner is off, and the bottom image is on high. In between, it'll go from low to medium to high temperatures.
The thing that goes wrong with these new temperature switches is that they lose the ability to switch. So when you turn the burner on, it only has the one speed, pedal to the metal.
I took out the switches on the two burners on my son's stove that weren't working and opened them up. The contacts inside were burnt and non-functional. Replacing both of the switches fixed the problem, and I strongly suspect that's what you'll find to be the issue on yours as well. Oh, just as a note, there were two different size burners used on my son's stove, and they took different replacement switches, so you might want to be aware of that.