Sensitivity analysis for optimal control problems subject to higher order state constraints

A family of parameter dependent optimal control problems is considered. The problems are subject to higher-order inequality type state constraints. It is assumed that, at the reference value of the parameter, the solution exi sts and is regular. Regularity conditions are formulated under which the or iginal problems are locally equivalent to some other problems subject to eq uality type constraints only. The classical implicit function theorem is ap plied to these new problems to investigate Frechet differentiability of the stationarity points with respect to the parameter.