On first order state constrained optimal control problems

Abstract

We show that exact penalization techniques can be applied to optimal control problems with state constraints under a hard to verify hypothesis. Investigating conditions implying our hypothetical hypothesis we discuss some recent theoretical results on regularity of multipliers for optimal control problem involving first order state constraints. We show by an example that known conditions asserting regularity of the multipliers do not prevent the appearance of atoms in the multiplier measure. Our accompanying example is treated both numerically and analytically. Extension to cover problems with additional mixed state constraints is also discussed