Computational optimal control of the terminal bunt manoeuvre - Part 2: Minimum-time case

This is the second part of a paper studies trajectory shaping of a generic cruise missile attacking a fixed target from above. The problem is reinterpreted using optimal control theory resulting in a minimum flight time problem; in the first part the performance index was time-integrated altitude. The 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. The formulation is solved using a three-stage approach. In stage 1, the problem is discretized, effectively transforming it into a non-linear programming problem, and hence suitable for approximate solution with DIRCOL and NUDOCCCS. The results are used to discern the structure of the optimal solution, i.e. type of constraints active, time of their activation, switching and jump points. 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 (TPBVPs), using the appropriate theorems of optimal control theory. The TPBVPs obtained from this indirect approach are then solved using BNDSCO and the results compared with the appropriate solutions of stage 1. The influence of boundary conditions on the structure of the optimal solution and the performance index is investigated. The results are then interpreted from the operational and computational perspectives.