The modal auxiliaries have no past participles and so don't have perfects of their own (although they can govern perfect infinitives).
So, "can", "will", "shall", "may" have past forms "could", "would", "should", "might", but no past participles (nor present participles, nor infinitives). However, even the past forms are more often used with non-past meaning than with past meaning, so some people prefer to think of them as separate verbs. (For example, "could" often refers to a future potential event, as do "would" and "might".)
"Must" and "ought" also lack past participles (and present participles and infinitives), but these two verbs only have a single tense form, with no present/past distinction even notionally.
So, the past of "I can" is "I could", but there is no present perfect or past perfect. If you needed one, you would have to use a workaround such as "I have been able to" (present perfect) and "I had been able to" (past perfect). For "must", the workarounds are "I have had to" (present perfect) and "I had had to" (past perfect).
Although the modal verbs have no perfects of their own, they can govern perfect infinitives, e.g. "I could have been", "I will have gone", "I would have known", "I might have done".