Hypersonic trajectories with control continuity constraints for adversarial games

Computing optimal solutions for unpowered hypersonic glide vehicle trajectories requires high degree of numerical sophistication, making the development of fast and robust in-flight retargeting capabilities a challenging problem. Toward that end, recent efforts use neural networks that are pretrained with representative sets of target states obtained offline. The ability to characterize trajectories over an entire operating envelope and adapt in-flight for potentially changing target conditions requires significant computational resources. In this context, the use of continuation methods becomes extremely attractive. For unpowered hypersonics, stabilized continuation in particular is appealing due to its ability to obtain solutions with poor initial guesses, automatically select continuation step sizes, and attenuate accumulated numerical error over the continuation interval. In this work, the usage of stabilized continuation for both two and three degree of freedom unpowered hypersonics is expanded for maximum terminal energy trajectories in the context of a two-player pursuit-evasion game between a hypersonic vehicle and an adversarial ground target. Additional constraints are defined which provide guaranteed control continuity as maneuvers to new terminal conditions occur in-flight throughout a game, ensuring a realistic flight path is maintained. An easy to compute measure for characterizing the reachable terminal conditions at any given time using stabilized continuation is developed and some numerical convergence conditions are discussed. To generate various simulation scenarios, strategic capabilities for each player are designed; these strategies also employ stabilized continuation in various manners to determine courses of action throughout the game. Algorithms for these strategies are expressed and their efficacy is discussed in the context of performance through miss distance and final velocity