sometimes, a lot of shifting problems come from too high of an idle speed. first off, make sure the idle speed it about 900 rpm to 1100 rpm, which the owners manuel will say. after the idle is set right, try and shift.
unfortunatly, these polaris quads have had a problem with the transmission shift gears and shafts bending and breaking if the bike was shifted while moving or too high of an idle speed. if the bike starts and runs, and you give gas an it does not move, then you have a drive line problem.
before you remove the transmission, check the drivebelt to make sure there is no problems in there. if the belt is too tight ot broken/binding up inside the clutches, that couldbe your problem as well. these transmissions come out of the chassis without pulling the engine, but there is a lot of difficulty removing it espically when it is a 4X4 model. you should let the experts handle this repair if it is the transmission.
to answer your question, the transmission is not controlled electronically, it only has a sensor that tells the gauge/ignition unit what gear it is in. the quad will limit speed and rpm in reverse, which is part of what the sensor does