Distributionally robust LQG control under distributed uncertainty

A new paradigm is proposed for the robustification of the LQG controller against distributional uncertainties on the noise process. Our controller optimizes the closed-loop performance in the worst possible scenario under the constraint that the noise distributional aberrance does not exceed a certa...

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Bibliographic Details
Published inAutomatica (Oxford) Vol. 174; p. 112128
Main Authors Falconi, Lucia, Ferrante, Augusto, Zorzi, Mattia
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.04.2025
Subjects
Dynamic programming
Optimal control
Relative entropy
Robustness
Stochastic systems
Robustness
Relative entropy
Dynamic programming
Stochastic systems
Optimal control
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Summary:A new paradigm is proposed for the robustification of the LQG controller against distributional uncertainties on the noise process. Our controller optimizes the closed-loop performance in the worst possible scenario under the constraint that the noise distributional aberrance does not exceed a certain threshold limiting the relative entropy between the actual noise distribution and the nominal one. The main novelty is that the bounds on the distributional aberrance can be arbitrarily distributed along the whole disturbance trajectory. This is a problem for which, notwithstanding significant attention given in the recent literature, so far only relaxed or approximated solutions have been derived. We denote this Distributed uncertainty Distributionally robust LQG problem with the acronym D2-LQG.
ISSN:0005-1098
DOI:10.1016/j.automatica.2025.112128