Research On Calculational Methods For Guided Bomb's Optimal Glide Trajectory

Trajectory optimization is one of the most important tasks in the research project of changing conventional bomb into guided bomb. The trajectory optimization's key factors have a meaningful significance on improving the performance of guided bomb's weapon system and implementing precision bombing far away from defence area. So this thesis mainly studies the numerical methods for the guided bomb's optimal glide trajectory problem.(1) In view of the inbeing of trajectory optimization problems, the methods for solving continuous-time optimal control problems were summarized. The numerical methods for the optimal control problems were introduced and classified as indirect methods and direct methods. Then two key steps of direct methods were pointed out. The first step of direct methods is transforming optimal control problems to parameter optimization problems, and the second step is solving the parameter optimization problems. And parameterization methods and parameter optimization methods were specially studied.(2) The researches on the problem of guided bomb's optimal glide trajectory were organized as:On the basis of reasonable hypothesis, the system motion equations of guided bomb in the vertical plane were establisded and became simplely dimensionless ones by introducing dimensionless variables. Then the optimal control mathematic model of guided bomb's optimal glide trajectory for maximum range was established.Indirect methods based on dynamic programming were presented. Firstly, the optimality condition for the trajectory optimization problem was analyzed. Then the steps of continuous differential dynamic programming were specially presented and orgnized. At last through algorithm implementation, it's shown that the continuous differential dynamic programming method can be utilized for the trajectory optimization problem. With results, the optimal glide characters for maximum range were analyzed and summarized.Direct methods for the trajectory optimization problem were presented. With the conclusions about direct methods, a direct method based on sequential quadratic programming and another one based on particle swam optimization were respectively proposed, according to two main respects: parameterization methods and parameter optimization methods. Then it's shown that the two direct methods are valid, through solving the trajectory optimization problem.(3) With results of numerical test, different numerical methods proposed in this thesis were compared about precision,efficency and robust property. And limitations of existing numerical methods for trajectory optimization were summarized. Then some advices about farther research are presented.