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Sensitivity-Driven Experimental Design to Facilitate Control of Dynamical Systems

Journal of Optimization Theory and Applications

van Bloemen Waanders, Bart G.; Hart, Joseph L.; Hood, Lisa G.; Parish, Julie M.

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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TYPE Journal Article YEAR 2023
DOIOSTIScopus

ENABLING HYPER-DIFFERENTIAL SENSITIVITY ANALYSIS for ILL-POSED INVERSE PROBLEMS

SIAM Journal on Scientific Computing

Hart, Joseph L.; van Bloemen Waanders, Bart G.

Inverse problems constrained by partial differential equations (PDEs) play a critical role in model development and calibration. In many applications, there are multiple uncertain parameters in a model that must be estimated. However, high dimensionality of the parameters and computational complexity of the PDE solves make such problems challenging. A common approach is to reduce the dimension by fixing some parameters (which we will call auxiliary parameters) to a best estimate and use techniques from PDE-constrained optimization to estimate the other parameters. In this article, hyper-differential sensitivity analysis (HDSA) is used to assess the sensitivity of the solution of the PDE-constrained optimization problem to changes in the auxiliary parameters. Foundational assumptions for HDSA require satisfaction of the optimality conditions which are not always practically feasible as a result of ill-posedness in the inverse problem. We introduce novel theoretical and computational approaches to justify and enable HDSA for ill-posed inverse problems by projecting the sensitivities on likelihood informed subspaces and defining a posteriori updates. Our proposed framework is demonstrated on a nonlinear multiphysics inverse problem motivated by estimation of spatially heterogeneous material properties in the presence of spatially distributed parametric modeling uncertainties.

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TYPE Journal Article YEAR 2023
DOIOSTIScopus
Results 1–25 of 185
Results 1–25 of 185