Towards the real-time application of indirect methods for hypersonic missions

Michael J Sparapany, Purdue University


Conceptual hypersonic mission design has typically been performed in a computationally intensive, iterative manner using direct optimization methods. The introduction of modern computing has resulted in the widespread adoption of direct methods, and useful information associated with optimal solutions has been lost. Optimization through indirect methods leverages this information, yielding high quality trajectories while reducing the dimensionality of the overall problem. The amount of content that can fit on a single chip is approaching physical limitations, resulting in state-of-the-art systems to use more chips. Due to this, present day computational systems are transitioning towards massively parallel frameworks thus creating a need for parallel algorithms to make effective use of available resources. The Multiple Shooting Method provides an effective means of constructing indirect solutions for hypersonic systems using parallel computational architectures. For systems with complex dynamics, it is expected that the chips will become fully saturated with computations, providing performance increases over the serial counterpart. One restriction to performing optimization using indirect methods is the requirement of high quality initial guesses that must be sufficiently close to a solution for convergence. Sophisticated nonlinear prediction models are used to overcome this limitation. Dimension reductions are performed using Noether's First Theorem with a generalization to Hamiltonian systems. A surrogate model is used to test and validate the outputs of the nonlinear prediction model are high-quality, thus increasing confidence in the constructed initial guess. The combination of parallel processing with generated high-quality initial guesses is shown to reduce the time to obtain a solution as well as increase the confidence that convergence to a solution will be obtained. Both these criteria must be known to perform real-time hypersonic optimization on-board a vehicle.




Grant, Purdue University.

Subject Area

Aerospace engineering

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