This is an excellent question and I will provide you with a few points to consider when analysing how characters change through the play. What is interesting to note is how the state of many characters change at the end of the play compared to their position at the beginning. The biggest change comes of course in Prospero, who begins the play as a powerful magician, which allows him to effectively stage manage the entire action of the play. He is shown to be completely in control, yet it is interesting that he gives up his magic art, and, we assume therefore, his power when he leaves the island and is restored to his former position.
Linked with the change in Prospero's status, we see a change in Ariel and Caliban. The removal of their master gives them a real change in status. Ariel is freed from his servitude and Caliban is left alone on the island that was his before Prospero came and is no longer going to be mistreated and abused by Prospero and the other men who visit the island. Likewise characters such as Alonso change through their ordeals on the island, and become humbled and realise how Prospero has been wronged through their actions.
Lastly, Ferdinand and Miranda, even though Miranda is Prospero's daughter, are not free from Prospero's control. They are carefully tested to show that they are ready for marriage and for love and their union at the end of the play indicates the transformation that they have undergone as characters.
So, you might like to approach this question by thinking about how characters change and develop from the beginning of the play to the characters we see at the end of the play.