And that document also spells out the conditions under which he may use those warpowers--namely, a DECLARED WAR. None of the so-called wars we are currently engaged in are declared wars. In fact the "War on Terror" is not even against an actual entity. If jihadists are our enemy, then why not declare war on jihadists? By defining it so loosely, anyone who is perceived as a terrorist is the enemy and therefore subject to the whimsical use of these warpowers by a vindictive, partisan president. That "terrorist" could be you or me.
With respect to the attack by the irredentists of the former Islamic Caliphate called "The Ottoman Empire", they declared war on us. Until they surrender and sue for a peace treaty we are at war with them.
The Constitution clearly establishes the fact that the President has an open ended right to repel invaders. "W" bothered getting an authorization to use force though.
Again unless you can come up with some Constitutionally prescribed piece of wording that says "Declaration of War" you will have to live with what the Constitution says on the matter.
Now, regarding peace, presumably the President can make a treaty with just about anybody ~ country or otherwise ~ and with 2/3 concurrence of the Senators present and voting, that becomes law.
In short, the President can stop fighting a war if and only if he has the concurrence of the Senate with a super majority. To that degree the Constitution has a clear BIAS toward continuing war ~ once engaged ~ which is something you should really think about. Not only do we give the President the authority to defend the nation once he starts doing that he's on the hook until a super majority in the Senate says he can stop taking those actions.
Currently that would include making war against any forces of any kind in any part of the Former Islamic Caliphate!