Publications Details

Jacobian Conditioned Two-Layer Stabilized Continuation for Computing Optimal Hypersonic Trajectories

Vedantam, Mihir; Akella, Maruthi R.; Grant, Michael J.

This paper presents the formulation and application of a Jacobian Conditioned Two-Layer Stabilized Continuation algorithm. Continuation methods typically require the designer to pick a continuation/homotopy path that is well-posed over the entire continuation interval. This work specifically aims to alleviate the hard requirement for the Jacobian to be well-conditioned through the judicious introduction of nonlinear tuning functions to the original continuation path. Qualitatively speaking, the new approach involves progressing along the homotopy path until the Jacobian exhibits numerical sensitivity or ill-conditioning. A new homotopy path is then selected through the introduction of additional nonlinearity to the continuation function. The Jacobian conditioned two-layer stabilized continuation algorithm is applied to the planar hypersonic reentry problem with a continuation path that violates the reachability envelope to showcase the powerful features of this new approach.