Subject-control verbs
Another way to think about it is as a subject complement.
The man (Subject) tried (verb) to run (infinitive) faster (Adverb).
The complement refers to the subject.
An example of an object complement would be:
The people chose the candidate who was tallest.
In this case, who was tallest? The object - the candidate.
In the first example, the subject is running.
I don't know if this helps but when I am stumped, I often try to substitute concepts or in some cases pronouns or tenses to test various grammatical problems or to help my comprehension.