Chance-Constrained Nonlinear Covariance Control via Robust Linearization Remainder Bounds
Abstract
When dealing with nonlinear systems, classical covariance steering typically propagates uncertainty via first-order linearizations, discarding higher-order Taylor remainders. This truncation causes computed statistical moments to diverge from the true physical state distribution, often leading to chance constraint violations. This paper introduces a discrete-time Sequential Convex Programming (SCP) framework that casts the deterministic one-step nonlinear numerical map as a Linear Stochastic Inclusion. The The Taylor remainder is modeled as a state-independent unstructured uncertainty block, bounded over a uniform envelope. The second-moment tubes are propagated via what we refer to as a robust Stochastic Linear Matrix Inequality (S-LMI) derived from the Petersen's lemma, providing an upper bound on the expected uncentered second moment. Domain-exit risk is bounded analytically via a Markov trace inequality, and spatial chance constraints are enforced via Gauss unimodal second-moment bounds within a Difference-of-Convex program. Simulations on a state-dependent nonlinear dynamic system demonstrate constraint satisfaction.
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BibTeX
@misc{koh2026chanceconstrained,
title = {{Chance-Constrained Nonlinear Covariance Control via Robust Linearization Remainder Bounds}},
author = {Man Jun Koh and Hyochoong Bang and SooJean Han},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.27742},
eprint = {2607.27742},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.27742},
}
RIS
TY - UNPB
TI - Chance-Constrained Nonlinear Covariance Control via Robust Linearization Remainder Bounds
AU - Man Jun Koh
AU - Hyochoong Bang
AU - SooJean Han
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2607.27742
UR - https://arxiv.org/abs/2607.27742
AB - When dealing with nonlinear systems, classical covariance steering typically propagates uncertainty via first-order linearizations, discarding higher-order Taylor remainders. This truncation causes computed statistical moments to diverge from the true physical state distribution, often leading to chance constraint violations. This paper introduces a discrete-time Sequential Convex Programming (SCP) framework that casts the deterministic one-step nonlinear numerical map as a Linear Stochastic Inclusion. The The Taylor remainder is modeled as a state-independent unstructured uncertainty block, bounded over a uniform envelope. The second-moment tubes are propagated via what we refer to as a robust Stochastic Linear Matrix Inequality (S-LMI) derived from the Petersen's lemma, providing an upper bound on the expected uncentered second moment. Domain-exit risk is bounded analytically via a Markov trace inequality, and spatial chance constraints are enforced via Gauss unimodal second-moment bounds within a Difference-of-Convex program. Simulations on a state-dependent nonlinear dynamic system demonstrate constraint satisfaction.
ER -