On the theory of exact penalizations for optimal control: new insights and refined conditions

We present developments within the theory of exact penalizations for solving optimal control problems with state constraints, focusing on two significant classes of problems that frequently arise in both theoretical analysis and practical applications. The theory provides a systematic procedure for reformulating constrained problems as equivalent unconstrained penalized problems. Two strategies are proposed, and their respective advantages, limitations, and distinctive features are discussed. Theoretical insights are illustrated through three representative examples.