Publications

Control of nonlinear dynamical systems is a complex and multifaceted process. Essential elements of many engineering systems include high-fidelity physics-based modeling, offline trajectory planning, feedback control design, and data acquisition strategies to reduce uncertainties. This article proposes an optimization-centric perspective which couples these elements in a cohesive framework. We introduce a novel use of hyper-differential sensitivity analysis to understand the sensitivity of feedback controllers to parametric uncertainty in physics-based models used for trajectory planning. These sensitivities provide a foundation to define an optimal experimental design which seeks to acquire data most relevant in reducing demand on the feedback controller. Our proposed framework is illustrated on the Zermelo navigation problem and a hypersonic trajectory control problem using data from NASA’s X-43 hypersonic flight tests.

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The generation of optimal trajectories for test flights of hypersonic vehicles with highly nonlinear dynamics and complicated physical and path constraints is often time consuming and sometimes intractable for high-fidelity, software-in-the-loop vehicle models. Practical use of hypersonic vehicles requires the ability to rapidly generate a feasible and robust optimal trajectory. We propose a solution that involves interaction between an optimizer using a low fidelity 3-DOF vehicle model and feedback from vehicle simulations of varying fidelities, with the goal of rapidly converging to a solution trajectory for a hypersonic vehicle mission. Further computational efficiency is sought using aerodynamic surrogate models in place of aerodynamic coefficient look-up tables. We address the need for rapidly converging optimization by analyzing how model fidelity choice impacts the quality and speed of the resulting guidance solution.

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