PID controller for dc - dc boost converter.

Is it possible to use ARDUINO for the closed loop pid control of a dc-dc boost converter ?

I don't see why not, although there are so many chips made that are designed to control boost converters that this would be an unusual thing to do. You could generate the signal to switch the output transistor from a PWM pin, and use the output from the PID to control the mark/space ration of the pin, with a limit to prevent the transistor being turned on for too much of the time.