Supercapacitors for Joint Strike Fighter?

Lockheed are reported to be having problems providing enough power for the F-35C Joint Strike Fighter which CSIRO's supercapacitors might fix. The F35 uses large amounts of electrical power short periods for the electro-hydrostatic flight control actuators to steer the plane. Lockheed's solution is a bigger generator, which will be under-used most of the time. The supercapacitors were developed by CSIRO to supplement batteries in electric cars, as capacitors can absorb power much quicker than a battery can.