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arXiv · 2503.13374

On Sampling Time and Invariance

Spencer Schutz·Charlott Vallon·Ben Recht·Francesco Borrelli
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Abstract

Invariant sets define regions of the state space where system constraints are always satisfied. The majority of numerical techniques for computing invariant sets have been developed for discrete-time systems with a fixed sampling time. Understanding how invariant sets change with sampling time is critical for designing adaptive-sampling control schemes that ensure constraint satisfaction. We introduce M-step hold control invariance, a generalization of traditional control invariance, and show its practical use to assess the link between control sampling frequency and constraint satisfaction. We robustify M-step hold control invariance against model mismatches and discretization errors, paving the way for adaptive-sampling control strategies.

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Spencer Schutz, Charlott Vallon, Ben Recht, Francesco Borrelli. 2025-03-17. On Sampling Time and Invariance. https://arxiv.org/abs/2503.13374

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