Solve the problem of optimal control to the origin for the system
where
I have done a bit, but Im not really sure where to go next....
Let
where
Then
where
Then
where
The costate equations are
so maximizes as a function of . As is linear in and then is maximized such that when and when
The eigenvalues are found when
when solving we have two eigenvalues
.
I'm not sure if what I have done is correct, and I don't know where to go from here.