Computational sensitivity analysis for state constrained optimal control problems

A theoretical sensitivity analysis for parametric optimal control problems subject to pure state constraints has recently been elaborated. The articles consider both first and higher order state constraints and develop conditions for solution differentiability of optimal solutions with respect to parameters. In this paper, we treat the numerical aspects of computing sensitivity differentials via appropriate boundary value problems. In particular, numerical methods are proposed that allow to verify all assumptions underlying solution differentiability. Three numerical examples with state constraints of order one, two and four are discussed in detail.