First, I love the banner. Such an intense flood of blue violet...
I'll weigh in on a possible ID and say I don't think your blooms are asters. They seem to lack the characteristic centers that all aster blooms display. Any aster I've ever seen has distinguishable floral disks, which your blooms seem to lack (or hide very well). Just google 'purple asters' and you'll see ample images of what I mean.
The foliage should help in deciding whether your plants are asters, too. Most of the asters I've seen have alternate leaves on the stems. They are single, not compound, usually narrow, and always pointed. They may or may not be serrated. You can get a sense of what I'm describing if you look at the foliage in Zoia's shot.
From what little I can see of the foliage in your plant, I'd have guess some kind of miniature chrysanthemum.
At the end of the day, knowing, or not knowing, their identity doesn't add to, or detract from one's enjoyment of them.
