These clauses are one of the most significant provisions in your recording arrangement, and you needed to understand both record deals and publishing to grasp the concepts. Since now you've got 'em both, let's do it. A controlled composition is a song written, owned, or controlled by the artist. However, it's usually defined more broadly than that, and includes:
1. Any song which the artist has an income or other interest. This means that, even if the artist doesn't own or control it, it's a controlled composition if he or she wrote or otherwise gets a piece of the earnings.
2. Sometimes. the definition also includes compositions owned or controlled by the producer of the recordings. You really have little, if any control over a producer's publishing, and thus you should try hard to get this provision out. It's hard to get rid of this, except at superstar levels, but do your best. I say this not only because it's difficult to get a producer to comply with it, but also because, with a producer of any importance, you could end up blowing your producing deal over it.