Distributionally Robust LQG with Kullback-Leibler Ambiguity Sets
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911083179016192 |
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| author | Fochesato, Marta Falconi, Lucia Zorzi, Mattia Ferrante, Augusto Lygeros, John |
| author_facet | Fochesato, Marta Falconi, Lucia Zorzi, Mattia Ferrante, Augusto Lygeros, John |
| contents | The Linear Quadratic Gaussian (LQG) controller is known to be inherently fragile to model misspecifications common in real-world situations. We consider discrete-time partially observable stochastic linear systems and provide a robustification of the standard LQG against distributional uncertainties on the process and measurement noise. Our distributionally robust formulation specifies the admissible perturbations by defining a relative entropy based ambiguity set individually for each time step along a finite-horizon trajectory, and minimizes the worst-case cost across all admissible distributions. We prove that the optimal control policy is still linear, as in standard LQG, and derive a computational scheme grounded on iterative best response that provably converges to the set of saddle points. Finally, we consider the case of endogenous uncertainty captured via decision-dependent ambiguity sets and we propose an approximation scheme based on dynamic programming. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08370 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Distributionally Robust LQG with Kullback-Leibler Ambiguity Sets Fochesato, Marta Falconi, Lucia Zorzi, Mattia Ferrante, Augusto Lygeros, John Optimization and Control Systems and Control The Linear Quadratic Gaussian (LQG) controller is known to be inherently fragile to model misspecifications common in real-world situations. We consider discrete-time partially observable stochastic linear systems and provide a robustification of the standard LQG against distributional uncertainties on the process and measurement noise. Our distributionally robust formulation specifies the admissible perturbations by defining a relative entropy based ambiguity set individually for each time step along a finite-horizon trajectory, and minimizes the worst-case cost across all admissible distributions. We prove that the optimal control policy is still linear, as in standard LQG, and derive a computational scheme grounded on iterative best response that provably converges to the set of saddle points. Finally, we consider the case of endogenous uncertainty captured via decision-dependent ambiguity sets and we propose an approximation scheme based on dynamic programming. |
| title | Distributionally Robust LQG with Kullback-Leibler Ambiguity Sets |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2505.08370 |