Abstract Efficient performance of a number of engineering systems is achieved through different modes of operation - yielding systems described as “hybrid”, containing both real-valued and discrete decision variables. Prominent examples of such systems, in space applications, could be spacecraft equipped with 1) a variable- I sp , variable-thrust engine or 2) multiple engines each capable of switching on/off independently. To alleviate the challenges that arise when an indirect optimization method is used, a new framework — Composite Smooth Control (CSC) — is proposed that seeks smoothness over the entire spectrum of distinct control inputs. A salient aftermath of the application of the CSC framework is that the original multi-point boundary-value problem can be treated as a two-point boundary-value problem with smooth, differentiable control inputs; the latter is notably easier to solve, yet can be made to accurately approximate the former hybrid problem. The utility of the CSC framework is demonstrated through a multi-year, multi-revolution heliocentric fuel-optimal trajectory for a spacecraft equipped with a variable- I sp , variable-thrust engine.

中文翻译：

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具有多种推进系统运行模式的最优轨迹设计的新方法，第 1 部分

摘要 许多工程系统的高效性能是通过不同的操作模式实现的——产生被描述为“混合”的系统，包含实值和离散决策变量。在空间应用中，此类系统的突出例子可能是配备 1) 可变 I sp 、可变推力发动机或 2) 多个发动机的航天器，每个发动机都能够独立打开/关闭。为了缓解使用间接优化方法时出现的挑战，提出了一种新框架——复合平滑控制 (CSC)，它在不同控制输入的整个范围内寻求平滑度。应用 CSC 框架的一个显着后果是，原始的多点边值问题可以被视为具有平滑的两点边值问题，可微分控制输入；后者显然更容易解决，但可以准确地逼近前者的混合问题。CSC 框架的实用性通过配备可变 I sp 、可变推力发动机的航天器的多年、多圈日心燃料优化轨迹得到证明。