On first order state constrained optimal control problems

Abstract

We show that exact penalization techniques canbe applied to optimal control problems with state constraintsunder a hard to verify hypothesis. Investigating conditionsimplying our hypothetical hypothesis we discuss some recenttheoretical results on regularity of multipliers for optimalcontrol problem involving first order state constraints. We showby an example that known conditions asserting regularity ofthe multipliers do not prevent the appearance of atoms in themultiplier measure. Our accompanying example is treated bothnumerically and analytically. Extension to cover problems withadditional mixed state constraints is also discussed