Optimal Control with Nonregular Mixed Constraints: An Optimization Approach

Abstract

We derive necessary conditions for optimality for control problems with smooth mixed constraints in the absence of regularity conditions. We show that the lack of regularity is reflected by the appearance of purely finitely additive set functions as multipliers corresponding to the mixed constraints. We illustrate with examples the rule of such set functions. Additionally, we show how our approach allows to treat regular mixed constraints and pure state constraints as particular cases; for the latter, we also provide a connection to well-established results involving only countably additive measures.