Rapid Simultaneous Hypersonic Aerodynamic and Trajectory Optimization Using Variational Methods

Traditional multidisciplinary design optimization methodologies of hypersonic missions often employ population-based global searching methods that rely on shooting methods to perform trajectory optimization. In this investigation, a rapid simultaneous hypersonic aerodynamic and trajectory optimization methodology is constructed based on variational methods. This methodology is constructed from two enabling advancements in analytic hypersonic aerodynamics and rapid trajectory optimization. Comparisons made with a single and multi-objective particle swarm optimizer highlight the computational advantages and improved solutions obtained through continuation of variational methods. The incorporation of trajectory constraints into the particle swarm optimization process through penalty functions or as additional objectives is shown to greatly increase the complexity of the design process. Alternatively, variational methods are able to precisely satisfy trajectory constraints without this added complexity. Examples demonstrate that Pareto frontiers in both vehicle and trajectory objectives can be constructed using variational methods. For convex frontiers, this is performed using a weighted sum of the objectives. For nonconvex frontiers, the optimization is performed through continuation of a set of constrained objectives.