Computational optimal control of the terminal bunt manoeuvre
This work focuses on a study of missile guidance in the form of trajectory shaping of a generic cruise missile attacking a fixed target which must be struck from above. The problem is reinterpreted using optimal control theory resulting in two formulations: I) minimum time-integrated altitude and 2) minimum flight time. Each formulation entails nonlinear, two-dimensional missile flight dynamics, boundary conditions and path constraints. Since the thus obtained optimal control problems do not admit analytical solutions, a recourse to computational optimal control is made. 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 I, the problem is discretised, effectively transforming it into a nonlinear programming problem, and hence suitable for approximate solution with the FORTRAN packages DIRCOL and NUDOCCCS. The results of this direct approach 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 I and optimal control theory, constitutes stage 2. Finally, in stage 3, the insight of stage 2 are made precise by rigorous mathemati cal 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 the FORTRAN package BNDSCO and the results compared with the appropriate solutions of stage I. For each formulation (minimum altitude and minimum time) 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. Software implementation employing DIRCOL, NUDOCCCS and BNDSCO, which produced the results, is described and documented. Finally, some conclusions are drawn and recommendations made.