The system where is not subject to any constraint, is to be controlled from to where is unspecified in such a way that
is minimized. Find the optimal control.
I have a solution, is there anyone who could check it and see if I have gone wrong somewhere?
Let
Let
Then where
The co-state equation is
By pmp, maximizes as a function of
The optimal trajectory is
and
which has general solution
Using the endpoint conditions
,
Therefore
Then, recalling that
We have
(recalling from above that from above)