A novel approach for optimal trajectory design with multiple operation modes of propulsion system, part 1

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. •Optimization of low-thrust interplanetary trajectories with variable specific impulse, variable thrust engines.•A new framework, called Composite Smooth Control (CSC), is developed to handle various types of state-triggered constraints.•Indirect optimization method is used to formulate fuel-optimal problems.•Complex-based derivative approach is used to construct co-state dynamics numerically.•Multi-revolution, multi-year trajectory optimization is analyzed.