Local infimum and a family of maximum principles in optimal control

The notion of a local infimum for the optimal control problem, which generalizes the notion of an optimal trajectory, is introduced. For a local infimum the existence theorem is proved and necessary conditions in the form of a family of ‘maximum principles’ are derived. The meaningfulness of the necessary conditions, which generalize and strengthen Pontryagin's maximum principle, is illustrated by examples.
Bibliography: 9 titles.