Solving Optimal Navigation Gain Programs For Pure Proportional Navigation

This paper presents a computational optimal control problem formulation for solving optimal gain programs for pure proportional navigation (PPN). The influence of 3 degree-of-freedom (DOF) missile flight dynamics is considered explicitly. The development provides an approach for exploring the optimality of conventional fixed-gain missile guidance laws (that consider missile kinematics only) and for extending the performance of conventional PPN. Algebraic constraint equations are utilized to sidestep computational challenges associated with the engagement equations. Furthermore, the navigation gain may be box-constrained to ensure that the solution retains sufficient control authority against an uncertain engagement. The results show that a fixed navigation gain is not acceleration optimal when 3-DOF missile flight dynamics are considered and that implementing an optimal gain program can be utilized to improve impact angles and/or acceleration margins as compared to fixed-gain PPN.