Inogen One, Sequal Eclipse, Airsep Lifestyle and others approved by the FAA
For a list of POCs that meet FAA specifications for inflight use see: www.faa.gov/about/initiatives/cabin_safety/portable_oxygen/
Portable oxygen concentrators (POCs) do not actually contain or generate oxygen, they concentrate it from the ambient air.
Those depending on a POC while traveling must bring sufficient spare batteries in carry-on baggage for the duration of the flight. Spare batteries must be protected from damage and short circuit.