Approximation of risk-averse optimal feedback control

The challenge of constructing feedback control laws for risk-averse optimal control of partial differential equations (PDEs) with random coefficients is addressed. The control objective composes a tracking-type cost with the nonlinear entropic risk measure. A sequential quadratic programming scheme...

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Bibliographic Details
Main Authors Guth, Philipp A, Kunisch, Karl
Format Journal Article
LanguageEnglish
Published 21.08.2025
Subjects
Mathematics - Optimization and Control
Online AccessGet full text
DOI10.48550/arxiv.2508.15618

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Summary:The challenge of constructing feedback control laws for risk-averse optimal control of partial differential equations (PDEs) with random coefficients is addressed. The control objective composes a tracking-type cost with the nonlinear entropic risk measure. A sequential quadratic programming scheme is derived that iteratively solves linear quadratic subproblems obtained through second-order Taylor expansions of the objective functional, with each subproblem re-centered at the previous iterate. It is shown that this method converges locally quadratically to the unique risk-averse optimal control. This work provides the first rigorous feedback synthesis for risk-averse objectives subject to PDEs with random coefficients.
DOI:10.48550/arxiv.2508.15618