A Study of Minimum Time-to-Climb Trajectories by Using a ParametricOptimization Method

• Main Authors: Kao-Sheang Liu, 劉高享
• Other Authors: Dong-Long Shue
• Format: Others
• Language: zh-TW
• Published: 2004
• Online Access: http://ndltd.ncl.edu.tw/handle/28599984486504411936

碩士 === 國立成功大學 === 航空太空工程學系碩博士班 === 92 === 　　Since the analysis of the optimal trajectories using the optimal control theory associated with the gradient method are numerically very difficult due to the convergence problem, often it can not be applied effectively to solve many typical problems, In this thesis, the parametric optimization method is applied to analyze the minimum time-to-climb trajectory. In this two-point-boundary-value problem(TPBVP), the performance index is the terminal time and the load factor is the control which is assumed to be a polynominal function of the time. The coefficients of the polynominal function are taken as a set of parameters to optimize the performance index. Accordingly, necessary conditions for optimality are derived as a set of nonlinear simultaneous algebraic equations which in combination with the terminal conditions are used for solving a set of parameters. In order to validate the theory, a numerical problem is given. With the given problem, the effects of initial conditions and final conditions on the mimnimum time-to-climb trajectories are investigated.