Trajectory Optimization And Simulation Of The Long-range Guided Rocket

In the modern warfare, range, accuracy and power are important performance indicators of the rocket, and the range, as the most important performance indicator, is paid more attention by all nations. With the rapid development of science and technology in the modern weapon, all nations are trying to use a variety of techniques to increase the range of the rocket effectively, and achieve mathematical strike in the long range. The ballistic flight used gliding flight is a way to increase the range of rocket, but because of the constraint conditions included the flight Mach number, running time of engines and the angle of emission, make the ballistic characteristics of ballistic flight become very complex. In the premise of satisfying the constraints, taken the range as the optimized index, the optimization technology of trajectory can give the optimal flight trajectory.The optimized design of trajectory in long-range guided rocket is studied in this paper, according to flight characteristics of the long-range guided rocket, and the whole trajectory is divided into the section with the same thrust, the section with the convertible thrust and glide section. It is given the general description of optimal control problem, and how to parameterize the optimal control problem and derivation of the gradient formula. To aim at Sequential Quadratic Programming method, the conditions Kuhn-Tucker (KT) are given. For the constrained problems, using quasi-Newton method proves the equivalence of a non-linear programming problem and a quadratic programming problem, and the solution for the non-linear programming problem is equivalent to the solution of the equivalent quadratic programming problem in the calculation of each iterative computation. To the updated matrix named Bk, using amended method named Broyden-Flecher-Goldfarb-Shanno(BFGS) for correction. Because of the drawbacks of the local convergence in Sequential Quadratic Programming method, the associated method combined penalty functions and one-dimensional search method is used to satisfy the global convergence, the corresponding solutions of no solution for Subproblems and Maratos effect are also given in this paper.Without considering the constraint condition of the rudder, taking the range as the optimized performance indicators, and taking the flight Mach number, launch angle, running hours of engines, thrust of engines, fuel of engines, the end of the height from the ground and trajectory angle as the constraints, the sequential quadratic programming is used to do optimized design and the mathematical simulation of the long-range guided rocket flight trajectory. Simulation results show that the designed trajectory with the same section of thrust, the section with the convertible thrust and glide section satisfies the performance requirements. It proves the correctness and feasibility of research methods of this paper.