note that the form: /ho sognato DI te/ is invariant, it never switches to: sognatA

In transitive verbs, the participle may agree with the object in gender and number. However, it's not mandatory: you can just use "sognato" or the singular masculine. I use, though not systematically, "sognato" also for feminine and plural objects, and I am a native speaker living in Italy, so I wouldn't say it's less correct.

ti ho sognato ==> I've dreamed of you ...where you ==> male ti ho sognata ==> I've dreamed of you ...where you ==> female ps. not sure about English translation, but I hope the meaning is clear.

correct: 1a) Io ho sognato Francesca. wrong: 1b) Io ho sognata Francesca. (Francesca is a female name) correct: 2a) Io ho sognato lei. wrong: 2b) Io ho sognata lei. correct: 3a) Io ti ho sognato. (when /tu/ = female or male) correct: 3b) Io ti ho sognata. (when /tu/ = female)