Second order sufficient conditions and sensitivity analysis for the optimal control of a container crane under state constraints

Stability and sensitivity analysis of parametric control problems has recently been elaborated for optimal control problems subject to pure state constraints. This]paper illustrates the numerical aspects of sensitivity analysis fbr a complex practical example: the optimal control of a container crane with a state constraint on the vertical velocity. The multiple shooting method is used to determine a nominal solution satisfying first order necessary conditions. Second order sufficient conditions are checked by showing that an associated Riccati equation has a bounded solution. Sensitivity differentials of optimal solutions are computed with respect to variations in the swing angle.