A singular perturbation analysis of optimal aerodynamic and thrust magnitude control

This paper illustrates the application of singular perturbation methods to optimal thrust magnitude control (TMC) and optimal lift control in flight mechanics. The modeling is restricted to horizontal plane dynamics. A multiple time scale analysis results in nonlinear feedback control solutions for lift and thrust during a turn to a specified down range position. The analysis is carried out to rust order with respect to the position state variables. Numerical results for a medium range and a short range air-launched missile are given, and comparisons are made to two alternative propulsion control concepts. The multiple time scaling procedure used here is applicable to solving a wide class of optimal control problems. It avoids the problem in asymptotic methods of picking the unknown adjoints to suppress unstable modes in the boundary layer and reduces the two-point boundary value problem to a series of pointwise function extremizations. Hence, the optimal control solution is essentially analytic and algebraic.