Energy management for a multiple-pulse missile

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Virginia Polytechnic Institute and State University


A nonlinear programming technique is applied to the optimization of the thrust and lift control histories for missiles. The first problem considered is that of determining the thrust history which maximizes the range of a continuously-variable (non-pulsed) thrust rocket in horizontal lifting flight. The optimal control solution for this problem is developed. The problem is then approximated by a parameter optimization problem which is solved using a second-order, quasi-Newton method with constraint projection. The two solutions are found to compare well. This result allows confidence in the use of the nonlinear-programming technique to solve optimization problems in flight mechanics for which no analytical optimal-control solutions exist. Such a problem is to determine the thrust and lift histories which maximize the final velocity of a multiple-pulse missile. This problem is solved for both horizontal- and elevation-plane trajectories with and without final time constraints. The method is found to perform well in the solution of these optimization problems and to yield substantial improvements in performance over the nominal trajectories.