Design And Implementation Of Optimization Based On Gaussian Trajectory Pseudo Spectrum

Trajectory optimization is the process of designing a trajectory that minimizes or maximizes some measures of performance within prescribed constraint boundaries. Excellent speed characteristic means a lot to the self-state and completion of the tactical tasks. So the velocity parameter should be paid more attentions. Especially in some trajectory optimization problems that are involved in the penetration ability of the missile, the dynamic pressure of missile and the special demands of velocity itself. Meanwhile the velocity relates to the structural load, actual overload and the stability of the missile. Hence, this paper takes the velocity as the key parameter to optimize the trajectory.A trajectory optimization problem is essentially the same as an optimal control problem in mathematics sense. This paper introduces the development status of methods of solving optimal control problem, expounds the main ideas and methods. The indirect method and the direct method are also compared in principle and characteristics to specifies the advantages and disadvantages. Some typical sub-methods belong to the two main methods are also introduced. Besides, a specific example was illustrated to specify the deficiencies of indirect methods. Then, this paper introduces the superiority of pseudospectral method compared with other direct methods and draws a conclusion that Gauss pseudospectral method(GPM) has more advantages than other common pseudospectral methods. This paper also expounded the ideas and procedure of solving the optimal problems in detail by using GPM.The treatises of solving optimization problems by pseudospectral methods mostly discuss on reentry vehicle. However, less attentions are paid on the missiles flying within the atmosphere. This paper solves the trajectory optimization problem within some endpoint and states constraint boundaries by GPM. After that, a reasonable trajectory was got by the GPOPS-II software.Finally, the test use method of standard position tracking and overload tracking to approximate the optimized trajectory. The simulation result shows that two methods were well recurred the optimized trajectory. At the end of this paper, some problems are presented during the study. Based on the current research results, the paper showed an outlook on the application of Gauss pseudospectral method in solving the optimal problems, especially in the field of real-time trajectory optimization.