Mathematics for Economists

Optimal control

Writing it back to the equationx =u

x(t)x( 0 )=

Zt

0

u(s)ds=

Zt

0

1

4

s^2 T^2

ds=

1

12 t

(^3) ^1
4 T
(^2) t.
As the Hamiltonian is concave in(x,u)it is a real maximum.