Arrieta-Camacho Juan José, Biegler Lorenz T
Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA.
Ann N Y Acad Sci. 2005 Dec;1065:174-88. doi: 10.1196/annals.1370.001.
Real time optimal guidance is considered for a class of low thrust spacecraft. In particular, nonlinear model predictive control (NMPC) is utilized for computing the optimal control actions required to transfer a spacecraft from a low Earth orbit to a mission orbit. The NMPC methodology presented is able to cope with unmodeled disturbances. The dynamics of the transfer are modeled using a set of modified equinoctial elements because they do not exhibit singularities for zero inclination and zero eccentricity. The idea behind NMPC is the repeated solution of optimal control problems; at each time step, a new control action is computed. The optimal control problem is solved using a direct method-fully discretizing the equations of motion. The large scale nonlinear program resulting from the discretization procedure is solved using IPOPT--a primal-dual interior point algorithm. Stability and robustness characteristics of the NMPC algorithm are reviewed. A numerical example is presented that encourages further development of the proposed methodology: the transfer from low-Earth orbit to a molniya orbit.
针对一类低推力航天器考虑实时最优制导。具体而言，利用非线性模型预测控制（NMPC）来计算将航天器从低地球轨道转移到任务轨道所需的最优控制动作。所提出的NMPC方法能够应对未建模的干扰。转移动力学采用一组修正的赤道元素进行建模，因为它们在零倾角和零偏心率时不会出现奇点。NMPC背后的思想是重复求解最优控制问题；在每个时间步，计算一个新的控制动作。最优控制问题使用直接方法求解——完全离散运动方程。离散化过程产生的大规模非线性规划使用IPOPT（一种原始对偶内点算法）求解。回顾了NMPC算法的稳定性和鲁棒性特征。给出了一个数值示例，鼓励对所提出的方法进行进一步开发：从低地球轨道到莫尼亚轨道的转移。
