Application of singular perturbation techniques (SPT) and continuation methods for on-line aircraft trajectory optimization

The singular perturbation theory (SPT) approximation of optimal feedback control laws is presented and methods for on-line application of these approximations are discussed. It is shown that SPT control laws break down when the current state is near the terminal target state. The use of continuation methods to improve the accuracy of the SPT approximation and to obtain global solutions of Two-Point Boundary Value Problems (TPBVP) is also discussed. To illustrate the theoretical discussion we present the minimum-time control of a supersonic aircraft for a three-dimensional intercept problem.