Mathematics for Economists

Optimal control

Example

Solve the problem

ZT

0

1 tx(t)u(t)^2 dt!max

x(t)=u(t), x( 0 )=x

0.

There is no boundary condition onx(T)that isx(T)is free. In this case

the transversality condition isp(T)= 0 .The Hamiltonian is

H(t,x,u,p)= 1 txu^2 +pu.