Mathematics for Economists

Optimal control

The optimal uis maximizes the Hamiltonian 2xx^2 +puover

U=[ 1 , 1 ]so

u(t)=



1 if p(t)> 0

1 if p(t)< 0.

Asx=uandu1 andx( 0 )= 0 x(t)<1 fort 2 ( 0 , 1 ).From the

adjoint equation

d

dt

p=Hx^0 = 2 x 2 = 2 (x 1 )< 0

sopis strictly decreasing.