Learning-Based Shrinking Disturbance-Invariant Tubes for State- and Input-Dependent Uncertainty

• URL: http://arxiv.org/abs/2601.11426v1
• Date: Fri, 16 Jan 2026 16:47:04 GMT
• Title: Learning-Based Shrinking Disturbance-Invariant Tubes for State- and Input-Dependent Uncertainty
• Abstract summary: We develop a learning-based framework for constructing shrinking disturbance-invariant tubes under state- and input-dependent uncertainty.<n>We certify safety via a lifted, isotone (order-preserving) fixed-point map.
• Score: 1.3750624267664155
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: We develop a learning-based framework for constructing shrinking disturbance-invariant tubes under state- and input-dependent uncertainty, intended as a building block for tube Model Predictive Control (MPC), and certify safety via a lifted, isotone (order-preserving) fixed-point map. Gaussian Process (GP) posteriors become $(1-α)$ credible ellipsoids, then polytopic outer sets for deterministic set operations. A two-time-scale scheme separates learning epochs, where these polytopes are frozen, from an inner, outside-in iteration that converges to a compact fixed point $Z^\star\!\subseteq\!\mathcal G$; its state projection is RPI for the plant. As data accumulate, disturbance polytopes tighten, and the associated tubes nest monotonically, resolving the circular dependence between the set to be verified and the disturbance model while preserving hard constraints. A double-integrator study illustrates shrinking tube cross-sections in data-rich regions while maintaining invariance.

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