An irrevocable trust is usually set up to for estate tax benefits and cannot be revoked.
You are, in essence, giving away the assets that are placed in this type of trust, but you specify the beneficiary, the purpose of the assets and income in the trust, and how they are to be used, thus, you still maintain some control of them but not physical control.
You cannot name yourself as the trustee but you can appoint someone you trust, such as a family member, friend, a trust company, an attorney or a bank.