The verb ask can take several different kinds of object complement clause.
By far the most common kind with ask is the infinitive complement, usually with Equi-NP-Deletion of the infinitive subject from the indirect object of ask:
- They asked us to perform a comprehensive survey.
i.e, us is the IO of ask, and also is the subject of perform, though it's not repeated.
However, if ask is only transitive (rather than bitransitive; i.e, no indirect object), it can take an untensed That-complement, which is a cross between an ordinary tensed That-complement and an infinitive complement.
It looks just like a regular That-complement, except it uses an infinitive (which has no tense -- that's what infinitive means) as the main verb.
- They asked that he write "No flowers, please" on the announcement.
notice, *he write, not he writes or he wrote; those are tensed.
Untensed That-complements are often called "Subjunctive" by those who
- have studied Latin
- have been taught by those who studied Latin
- have been taught by someone taught by someone who studied Latin
etc, d.c. al fine.
because Latin had a subjunctive mood that is sometimes used in some of the same ways as the English untensed That-complement is. The term has become attached to the meaning in English, instead of to the grammar. That's why you probably never heard of an untensed That-complement before.
In the sentence given, (in brief)
- The city council has asked that a comprehensive survey be performed...
the complementizer that has been deleted, as it almost always is with object complements. (Note, incidentally, that the first auxiliary verb in the complement clause -- which takes the tense if there is any -- is be, the infinitive form).
The sentence would be clearer with the that left in. And the rest of the sentence is way too complex, with far too many subordinate clauses and marker deletions. If clarity is the object, make them all separate sentences, or at least put back some clause markers.