Mathematics for Economists

Optimal control

Example

Solve the problem

Z 1

0

2 x(t)x^2 (t)dt!max

x(t)=u(t), x( 0 )= 0 ,x( 1 )= 0 ,u(t) 2 [ 1 , 1 ].

The Hamiltonian is

H(t,x,u,p) = 2 xx^2 +pu.

d

dtp = H

x^0 =^2 x^2.

As there is a terminal condition onxthere is no transversality condition on

p.