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Distributionally Robust GMM Steering Under Wasserstein Ambiguity Sets
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DOI：10.1109/LCSYS.2026.3657859.png)
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Abstract
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This letter addresses the problem of steering a discrete-time linear system from an initial Gaussian Mixture Model (GMM) distribution, where the component weights are uncertain, to a prescribed terminal Gaussian distribution. We formulate a distributionally robust optimal control (DRO) problem by modeling the weight uncertainty via a Wasserstein-type ambiguity set. The resulting non-convex min-max problem is shown to be equivalently transformed into a tractable, deterministic Semidefinite Program (SDP) by leveraging duality theory and convex lifting techniques. The standard nominal (non-robust) controller can fail to satisfy terminal constraints under plausible worst-case weight distributions within the ambiguity set. In contrast, the proposed DRO controller successfully guarantees constraint satisfaction in these scenarios, demonstrating its improved robustness.
Keywords:
Uncertainty
Costs
Vectors
Symmetric matrices
Optimal control
Optimization
Gaussian distribution
Standards
Robustness
Measurement
distributionally robust optimization
Gaussian mixture models
semidefinite programming
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2
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94
Citations:
5.0K
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