Abstract
This paper uses the penalty function method to solve constrained optimal control problems. Under suitable assumptions, we can solve a constrained optimal control problem by solving a sequence of unconstrained optimal control problems. In turn, the constrained solution to the main problem can be obtained as the limit of the solutions of the sequence. In using the penalty function 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. Here we establish an existence theorem for those problems. Two numerical examples are presented to demonstrate the findings.