PreprintCC BY-NC-ND 4.0HAL
Beyond Ellipsoids: Semi-Algebraic Tightening for Chance Constraints Under Actuator Saturation
Abstract
Motivated by stochastic model predictive control applications, we develop a semialgebraic framework for constraint tightening in chance-constrained systems with unbounded additive disturbances and saturated inputs. The saturation nonlinearity is represented exactly through its semialgebraic description. A polynomial Lyapunov function satisfying a stochastic drift condition is then synthesized using sum-of-squares optimization, yielding finite-time probabilistic reachable sets and probabilistic ultimate bound. The resulting sets are further optimized through an objective tailored to constraint tightening. Numerical examples illustrate the effectiveness and scalability properties of the approach.
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BibTeX
@misc{karam2026beyond,
title = {{Beyond Ellipsoids: Semi-Algebraic Tightening for Chance Constraints Under Actuator Saturation}},
author = {Carlo Karam and Mirko Fiacchini and Matteo Tacchi-Bénard},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.19639},
eprint = {2607.19639},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05700372v2},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Beyond Ellipsoids: Semi-Algebraic Tightening for Chance Constraints Under Actuator Saturation
AU - Carlo Karam
AU - Mirko Fiacchini
AU - Matteo Tacchi-Bénard
PY - 2026
DA - 2026/09/26
PB - HAL
DO - 10.48550/arxiv.2607.19639
UR - https://hal.science/hal-05700372v2
AB - Motivated by stochastic model predictive control applications, we develop a semialgebraic framework for constraint tightening in chance-constrained systems with unbounded additive disturbances and saturated inputs. The saturation nonlinearity is represented exactly through its semialgebraic description. A polynomial Lyapunov function satisfying a stochastic drift condition is then synthesized using sum-of-squares optimization, yielding finite-time probabilistic reachable sets and probabilistic ultimate bound. The resulting sets are further optimized through an objective tailored to constraint tightening. Numerical examples illustrate the effectiveness and scalability properties of the approach.
ER -