C182 pilot reported the failure to open the crossfeed valve for the fuel tanks potentially led to the engine to begin sputtering and returned to normal after switching fuel tanks. ATC was advised of the power loss and gave the pilot priority handling.

Narrative

After completing my mission; I was on course back to ZZZ. My location was between ZZZ1 and ZZZ2; 20 miles west of ZZZ. I contacted ZZZ Approach Radar and told them my intentions for inbound landing. After I contacted Radar; my engine starting to sputter. I performed emergency procedures on the engine problem. I contacted ZZZ3 Radar and told them that I had a sputtering engine and still had fuel on board. I noticed my fuel selector valve was on the right fuel tank so I switched the valve to both fuel tanks. The engine started to run smoothy again. I also noticed there were 16 gallons of fuel in the left tank. ZZZ3 Radar closed the airspace and gave Aircraft X full control to do whatever was necessary to get down safely.Initially; Tower suggested we land on Runway XX. ZZZ3 Radar said the winds were from 210 at 12 - 20 kt. I contacted the Tower and requested to land on Runway XY due to Runway XX having strong tailwinds. ZZZ3 Tower approved for me to land on Runway XY. Aircraft X landed safely at ZZZ; wheels down at XA:38. All aircrew were safe. To prevent this situation from ever happening again; I will be more aware of the fuel tank status.