Applications of the exterior penalty method in constrained optimal control problems

This paper gives a theoretical analysis of the applications of the exterior penalty method in continuous-time non-linear programs and constrained optimal control problems. As an example, the Cauchy Inequality in the continuous case is proved. Also, the exterior penalty method is used to treat constrained optimal control problems. It is proved, under suitable assumptions, that a constrained optimal control problem can be solved by performing a sequence of unconstrained optimal control problems, and the constrained solution to the constrained optimal control problem can be obtained as the limit of the solutions to the sequence of unconstrained optimal control problems. In using the exterior penalty method to solve constrained optimal control problems it is usually assumed that each of the modified unconstrained optimal control problems has at least one solution. An existence theorem for these problems is also given.