On the General Concept of the Structure of an Optimal Control

摘要

In this paper, a system of axioms of a certain algebraic structure is proposed. This system reflects the property of being partially ordered for a set of admissible motions of a control system. The metric approach to the general optimal control problem is developed on this basis. This approach essentially uses the concept of partition of admissible motions and the new concept of a "secondary metric." Several theorems on necessary and sufficient optimality conditions are stated and proved in terms of these concepts.