A singular perturbation analysis of optimal thrust control with proportional navigation guidance

This paper derives a nonlinear optimal thrust control law for a missile using proportional navigation guidance to intercept a maneuvering target. It is shown that using singular perturbation techniques combined with a multiple time scaling approach leads to a control solution that has an algebraic feedback form. A state transformation (similar to the energy state transformation used in aircraft analysis) that can be used to extend the analysis is also derived. Numerical results are given for a short range air-launched missile, and comparisons are made to proportional navigation guidance with boost-coast propulsion. The results show that optimal TMC greatly improves performance for missile launches at high aspect angles relative to the target velocity vector, and when launching from a lag condition relative to the line-of-sight.