I have been scouring multiple books on dynamic optimization, and read and studied multiple from beginning to end, including Liberzon's and Chiang's books.
All these books have sections on
free endpoint problems
infinite horizon problems
problems with inequality integral constraints.
However, none of them have anything on problems that have all three of these traits. It so happens to be that the combination of these three confuses me.
I'm wondering if there is any resource that analyses such a problem in a mathematically rigorous way?