The Exact Penalty Function Method in Constrained Optimal Control Problems

This paper uses the exact penalty function method to transform a constrained optimal control problem into an unconstrained one and establishes an equivalence between the two problems in the "local" sense. Necessary and sufficient condi tions are obtained for a penalty function to be exact. This generalizes the result of Xing et al. (J. Optim. Control Appl. Methods10(2) (1989), 173-180) where only sufficient conditions are obtained. As a by-product, the relationship between a penalty function and a stationary point is also established.