부산대학교 도서관

The concept of stratified necessary conditions for an optimal control problem, whose dynamic constraint is formulated as a differential inclusion, was recently introduced by F. H. Clarke. These are conditions satisfied by a (feasible) state trajectory that achieves the minimum value of a cost function, not over all state trajectories, but just ones whose velocities lie in a time-varying open ball of specified radius about the velocity of the state trajectory of interest. Considering different radius functions stratifies the interpretation of ‘minimizer’. In this paper we announce extensions of currently available stratified necessary conditions, to allow for the presence of a unilateral state constraint. As was shown by Clarke in the state constraint-free case, we find that, also in our more general setting, the stratified necessary conditions yield generalizations of earlier necessary conditions for unbounded differential inclusions as simple corollaries.