In a dramatic monologue, the speaker of the poem is not the poet. The speaker addresses an unknown listener/audience. Through the monologue, the reader may or may not determine who that audience is. The speaker reveals his/her temperament, some emotion and as such, the dramatic monologue is like a confession. Even though the speaker in a dramatic monologue is traditionally not the poet, Tennyson did say that "Ulysses" expressed his own impulse to carry on after the death of his friend Arthur Hallam.
Ulysses voices his frustration and restlessness with his "retirement." He is still a king and therefore he still has things to do, but he longs for adventure. He equates his relatively sedentary life with decay:
How dull it is to pause, to make an end,
To rust unburnished, not to shine in use! (22-23)
Ulysses then says, "As though to breathe were life!" It is not enough to be alive in order to appreciate life. Ulysses needs to embrace life to the fullest and give in to his adventurous impulses. He recognizes that his son, Telemachus, is more suited to settle down. Ulysses needs adventure; otherwise, he feels that he is simply allowing himself to decay.
However, Ulysses does give a rousing speech in which he hopes to find adventure again.
We are not now that strength which in old days
Moved earth and heaven, that which we are, we are-
One equal temper of heroic hearts,
Made weak by time and fate, but strong in will
To strive, to seek, to find, and not to yield. (66-70)
Ulysses begins the monologue complaining about his old age and his stationary life. He wallows in this frustration but ends the monologue with a motivational speech to his men (and to himself). He ends the monologue with the hope that his adventure has not or will not end. The transition from despair to hope is optimistic but it is a hope that Ulysses seems to be clinging to, reaching for. The reader can't help but be empathetic to Ulysses and urge him to adventure again (despite the fact that this would mean leaving his wife again, but that is another discussion).