Computational optimal control of the terminal bunt manoeuvre - Part 1: Minimum altitude case

S. Subchan*, R. Zbikowski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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, and hence suitable for approximate solution 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 are then solved using BNDSCO and the results compared with the appropriate solutions of stage 1. 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.

Original languageEnglish
Pages (from-to)311-353
Number of pages43
JournalOptimal Control Applications and Methods
Issue number5
Publication statusPublished - 2007
Externally publishedYes


  • Direct collocation
  • Direct method
  • Indirect method
  • Optimal control
  • Terminal bunt manoeuvre


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