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Optimization of Minimum-Time Low-Thrust Transfers Using Convex Programming

机译：使用凸规划优化最小时间低推力传递

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摘要

In this paper, a convex optimization method for the numerical solution of the minimum-time low-thrust orbit transfer problem is presented. The main contribution is the transformation of the free-final-time low-thrust trajectory optimization problem into a sequence of convex optimization problems. First, a new independent variable is introduced to rewrite the equations of motion, and a nonlinear optimal control problem is obtained. Then, the nonlinearity in the dynamics is reduced through a change of variables. By applying a lossless convexification technique, the nonconvex control constraints are convexified, and an equivalent problem is formed. The equivalence of the relaxation and the existence of the solution to the relaxed problem are proved. Based on the linearization of the dynamics, a successive convex approach is developed, and in each iteration, a second-order cone programming problem is solved efficiently by state-of-the-art interior-point methods. The effectiveness of the proposed method is verified through numerical simulations of an Earth-to-Mars low-thrust transfer problem. Furthermore, the performance of this convex approach is demonstrated by comparing with a general-purpose optimal control solver for transfers with multiple revolutions.
机译：针对最小时间低推力轨道传递问题的数值解，提出了一种凸优化方法。主要贡献是将自由时间的低推力轨迹优化问题转化为一系列凸优化问题。首先，引入一个新的自变量来重写运动方程，并获得非线性最优控制问题。然后，通过改变变量来减少动力学中的非线性。通过应用无损凸化技术，凸化了非凸控制约束，并形成了一个等效问题。证明了松弛的等价性和松弛问题的解的存在性。基于动力学的线性化，开发了一种连续凸方法，并且在每次迭代中，都通过最新的内点方法有效地解决了二阶锥规划问题。通过对地-火星低推力传递问题的数值模拟，验证了该方法的有效性。此外，通过与用于多转传输的通用最优控制求解器进行比较，证明了这种凸方法的性能。

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  • 来源
    《Journal of Spacecraft and Rockets》 |2018年第3期|586-598|共13页
  • 作者

    Wang Zhenbo; Grant Michael J.;

  • 作者单位

    Purdue Univ, Sch Aeronaut & Astronaut, W Lafayette, PA 47907 USA;

    Purdue Univ, Sch Aeronaut & Astronaut, W Lafayette, PA 47907 USA;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
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