Is there a special mitzvah to love one's parents?
If so, does it require the parent's awareness of that love?
Considering the fact that the Torah only writes of one's relationship to one's parents in terms of fear and respect, it would seem that the answer is no (note this Rabbi's answer's bold sentence).
The Chayei Adam, however, writes in the beginning of the Laws of Honoring Parents:
Based on a Zohar, a person should have the perspective that honoring his parents is similar to honoring God. Therefore, aside from the general mitzvah of loving one's fellow Jew, just as a person has a special mitzvah to love God, there is, by extension, a special mitzvah in loving one's parents.
In addition, loving one's parents makes sense in light of the obligation to respect them, because loving them makes doing the necessary services for them much easier. Anything that helps one do mitzvos is a good thing .