When he starts getting louder, get up and see if he wants you to follow him. There may be something he wants you to check out.
Keep your ears open around 11 too. You may have a neighbor who comes in around that time. Or, maybe in his previous life, that's the time his owner came home . . . If you can't find any kind of external reason for him to be barking, try to get him distracted a little before 11 each night - before the barking stops.