Mathematics for Economists

Optimal control

DeÖnition

The problem

Zt 1

t 0

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

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

0 )=x 0

u(t) 2 U,

is called the optimal control problem. The variablex(t 1 )can be Öxed or

free. The setUis called the control region.