Parametric sensitivity analysis:: A case study in optimal control of flight dynamics

Realistic optimal control problems from flight mechanics are currently solved by sophisticated direct or indirect methods in a fast and reliable way. Often one is not only interested in the optimal solution of one control problem, but is also strongly interested in the sensitivity of the optimal solution due to perturbations in certain parameters (constants or model functions) of the process. In the past this problem was solved by time-consuming parameter studies: A large number of almost similar optimal control problems were solved numerically. Sensitivity derivatives were approximated by finite differences. Recently a new approach, called parametric sensitivity analysis, was adapted to the direct solution of optimal control processes [3]. It uses the information gathered in the optimal solution of the unperturbed (nominal) optimal control problem to compute sensitivity differentials of all problem functions with respect to these parameters. This new approach is described in detail for an example from trajectory optimization.