Approximation of risk-averse optimal feedback control
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916911403499520 |
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| author | Guth, Philipp A. Kunisch, Karl |
| author_facet | Guth, Philipp A. Kunisch, Karl |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_15618 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximation of risk-averse optimal feedback control Guth, Philipp A. Kunisch, Karl Optimization and Control 49J20, 49N35, 93B52, 93C20 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. |
| title | Approximation of risk-averse optimal feedback control |
| topic | Optimization and Control 49J20, 49N35, 93B52, 93C20 |
| url | https://arxiv.org/abs/2508.15618 |