Free-Final-Time TPBVP/generalized BVP

[BenChung]

A common problem in optimal control is when you want to achieve some objective state but do not have a specific time by which that objective must be attained. One example of such a problem would be rocket landing guidance ("we want to land at a point without running out of fuel, but don't care about how long it takes"). A similar problem for a generalized BVP with intermediate state constraints is when the system needs to attain an intermediate point at some time, such as to go through a waypoin.

Right now, as far as I'm aware, this needs to be ``baked into'' the problem; you can build in a time dilation parameter into your model that maps a virtual time as proposed to BVP to real-world time which can then be optimized over by the solver. This is not general, though, and doesn't take advantage of solver adaptation.

It would be useful then to have an interface by which free-final-time could be specified in a BVProblem/TPBVProblem and then be solved taking advantage of adaptation.