2005 Cadillac STS Northstar shut down

This is the second time this has happened. When I pushed the car hard off the line, the engine initially accelerated but after a couple of seconds it sputtered and shut itself down - don't know if the engine was completely off, but the car came to a stop and I had to shut the car off and restart. Afterwards it seemed to run fine but engine light was on when I parked it. I have other situations when the car "jerked" upon harder acceleration. What would be causing this and how can it be fixed. I bought this car for the acceleration and it is just not performing at the moment.

Thanks,
Ben