Optimal Trajectory for a Hypersonic Scramjet Missile with a Non-Convex Control Set

Optimal control problems (OCPs) have wide-ranging applications across various industries, including aerospace technologies. Currently, there is significant interest in Hypersonic Cruise Missiles (HCMs) as cutting-edge weapons developed by major military powers. This study focuses on solving the maximum range OCP for such a missile. The chosen controls are the angle-of-attack (AOA) and fuel flow of the Scramjet engine. This research is the first to address the maximum range problem with a unique relationship between the controls, allowing the engine to make decisions regarding activation or deactivation. When the engine is activated, the AOA must be limited due to engine limitations, but when deactivated, a larger AOA is enabled.

The suggested relation is expressed as Vanishing Constraints, where the control set becomes non-convex, and the linear independent constraint qualification is failing, making it challenging to solve. To overcome this problem, we present a modified variable time transformation (VTT) method to deal numerically with these problems.

The HCM problem with the suggested relation was solved using the VTT and by directly implementing the OCP into existing optimization software. Both methods yielded very similar trajectories, confirming the VTT’s validity. All the problems were solved numerically using the FALCON optimization tool.