First-Order Necessary Conditions in Optimal Control

Abstract In an earlier analysis of strong variation algorithms for optimal control problems with endpoint inequality constraints, Mayne and Polak provided conditions under which accumulation points satisfy a condition requiring certain optimality function, used in the to generate search directions, be nonnegative all controls. The aim this paper is clarify nature condition, we call first-order minimax related integrated form which, also, implicit past algorithm convergence analysis. We consider these conditions, separately, when pathwise state constraint is, not, included problem formulation. When there are no show that equivalent minimum principle (and condition) strictly stronger than condition. For establish are, once again, equivalent. But, constrained context, it longer case or vice versa. An example confirms perhaps surprising fact distinct can provide information, some circumstances fails do so.