Are there any major English grammar books (like CGEL, PEU, etc.) that list "adjective complements" as one of main constituents of a predicate (or a sentence pattern)?
An adjective complement (also called an adjective phrase complement) is a phrase or clause that provides information necessary to complete an adjective phrase’s meaning. They are most often used with predicative adjectives (adjectives that follow linking verbs to describe the subject of the clause.
They seem a little concerned about the direction we’re taking.” (About the direction we’re taking is the complement of the adjective concerned.)
“She is skilled at archery.” (At archery is the complement of the adjective skilled.)
“The bosses are pleased with your progress.” (With your progress is the complement of the adjective pleased.)
“I’m very happy to know you!” (To know you is the complement of the adjective happy.)
“We’re just glad to be of service.” (To be of service is the complement of the adjective glad.)