Singular perturbation methods for variational problems in aircraft flight

The solution of variational problems by singular perturbation methods is discussed. In addition to the benefits of order reduction, these methods also can serve as practical devices for treating the singularities arising in problems where the control appears linearly and/or in state-constrained control problems. Furthermore, approximate feedback solutions can be derived for problem formulations that currently result in a nonlinear two-point boundary value problem. To illustrate an application, a feedback solution for aircraft, three-dimensional minimum lime turns is derived and discussed. Numerical results are presented for an F-106 and an F-4E aircraft.