Abstract: The problem of optimization is to find out the solution of extreme value，the calculus of variations is a kind of method to solve the functional extreme value. According to functional extreme theorems of second derivative at movable boundary condition，the author extends the functional extreme value problem of high-order derivative at movable boundary condition，then the author gives out the necessary condition and the proof of optimal control of high-order system with movable boundary.

Key words: functional variation, movable boundary condition, high-order system, optimal control