Mathematics for Economists

Optimal control, Bolza problem

We can also write as

Z 1

0



xx

 2

+ 2 xx dt =

Z 1

0

x^2 +x^2 dt!min,x( 0 )= 1.

The EulerñLagrange equation is

d

dt

2 x= 2 x = 2 x,xx= 0.

The characteristic equation isλ^2  1 =0 and the roots are 1 .The

general solution is

x(t)=C 1 exp(t)+C 2 exp(t).