# A Novel Approach for Optimal Trajectory Design with Multiple Operation Modes of Propulsion System, Part 1

arXiv: https://arxiv.org/abs/1910.09109 · HTML: https://mlsanity.com/paper/1910.09109/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Oct 2019.

## Built on by (most cited first, 1 of 1)

- [Advances in Trajectory Optimization for Space Vehicle Control](https://mlsanity.com/paper/2108.02335/) (2021)

## Abstract (arXiv)

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-Isp, 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-Isp, variable-thrust engine.