The Cig lighter circuit will probably not have enough juice for a 400w invertor: the PS3 draws 3.2 Amps@120v. this is equal to 384 watts (you might want a more powerfull invertor than 400w). Overhead aside, to provide 384 watts of power, the invertor will need to draw 32 Amps (at 12 Volts) - a cig lighter fuse is usually only 10 Amps. You might want to wire the invertor directly to the battery, and either put a rocker switch in, or hook it up with a relay attached to the cig lighter circuit.
Just my $.02
