Computational optimal control of the terminal bunt manoeuvre – Part 1: minimum altitude case

This two-part paper studies trajectory shaping of a generic cruise missile attacking a fixed target from above. This guidance problem is reinterpreted using optimal control theory resulting in two formulations: (1) minimum time-integrated altitude (part 1) and (2) minimum flight time (part 2). Each formulation entails non-linear, two-dimensional (vertical plane) missile flight dynamics, boundary conditions and path constraints, including pure state constraints. The focus here is on informed use of the tools of computational optimal control, rather than their development. Each of the formulations is solved using a three-stage approach. In stage 1, the problem is discretized, effectively transforming it into a non-linear programming problem. The results are used to discern the structure of the optimal solution. This qualitative analysis, employing the results of stage 1 and optimal control theory, constitutes stage 2. Finally, in stage 3, the insights of stage 2 are made precise by rigorous mathematical formulation of the relevant two-point boundary value problems. The results are then interpreted from the operational and computational perspectives.