变分法在控制中的应用

his paper mainly introduces the basics of variational method and it's application in optimal control problems of physics and economics. This article briefly introduces the background and significance of variational method, and then, it details the conclusions related to the calculus of variations. We finally will give the applications of optimal control problems and propose three specific models. The first one develops optimal mathematical model on the problems of the steepest fall in condition of non-obstructing free fall and obstructing free fall and shows how to solve them. The second is the classical Evans of the monopoly of the dynamic optimization model. The last one is a compromise problem between inflation and unemployment issues. All in all, we systematically master the basic theory of the calculus of variations and understand that it plays an important role about variational method in solving the practical optimal control problems.