Mathematics for Economists

Optimal control

Example

The problem

Zt 1

t 0

f(t,x(t),u(t))dt!max

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

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

is an optimal control problem. Observe that in this case there is a

restriction onx.The control region isU=[ 0 , 1 ].