Mathematics for Economists

Optimal control

If there is no restriction onu 2 Uthen to optimize the Hamiltonian with

respect touit is necessary thatHu= 0.

Hu^0 = 2 u+p= 0 , )u=p/ 2.

The adjoint equation is

d

dt

p(t)=H^0 x=t, p(T)= 0.

From this

p(t)=

1

2 t

(^2) +C=^1
2

t^2 T^2

.

This implies that

u(t)=^14

t^2 T^2

.