Chance-Constrained Nonlinear Covariance Control via Robust Linearization Remainder Bounds
arXiv:2607.27742
The paper proposes a sequential convex programming method that bounds Taylor remainders to improve covariance steering for nonlinear systems under chance constraints, using robust stochastic LMIs and analytical risk 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 Taylor remainder is bounded within an unstructured uncertainty block 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.
Accepted to 65th IEEE Conference on Decision and Control