First off, if you are not nervous or anxious before a performance, either you are not human or you don't care. I assume you are human... !
I realise that this will sound unbelievably trite, but: remember that no performance will ever be perfect. Particularly, don't be misled by recordings, particularly professional recordings -- they are edited to get rid of the mistakes! That said, also remember that your audience is there (at least most of them!) to enjoy the music you will give them. They are not there to tally up the slightly odd tempo bits, or the dynamic which didn't quite go the way you wanted, or even the C# which should have been a D#.
Know your music. Not just technically, but what it says to you and what you want to say with it. I have no doubt that you will have practiced enough so that you can and do, pretty much every time, play things the way you want to in the practice room.
Then... tell yourself that in your performance you have something you want to say to the folks out there, and go out and say it. You are not trying to prove anything!
Easier said than done. But it will get easier with more performing -- which suggests another point: try to perform most of your rep. in an informal setting from time to time. At some point you will get to the point where you are simply not aware of the audience at all, once you sit down and start to play (and yes, it took me years to get there!).