Nondegenerate necessary conditions for nonconvex optimal control problems with state constraints

Standard versions of the maximum principle for optimal control problems wit h pathwise state inequality constraints are satisfied by a trivial set of m ultipliers in the case when the left endpoint is fixed and lies in the boun dary of the state constraint set, and so give no useful information about o ptimal controls. Recent papers have addressed the problem of overcoming thi s degenerate feature of the necessary conditions. In these papers it is typ ically shown that, if a constraint qualification is imposed, requiring exis tence of inward pointing velocities, then sets of multipliers exist in addi tion to the trivial ones. A simple, new approach for deriving nondegenerate necessary conditions is presented, which permits relaxation of hypotheses previously imposed, concerning data regularity and convexity of the velocit y set. (C) 1999 Academic Press.