Chance-Constrained Covariance Steering in a Gaussian Random Field via Successive Convex Programming

TL;DR

This paper introduces a convex optimization-based method for designing affine feedback laws that steer the mean and covariance of uncertain systems affected by Gaussian random fields, ensuring chance constraints are satisfied.

Contribution

It develops a successive convex programming approach to handle chance-constrained covariance steering in spatially-dependent Gaussian disturbances.

Findings

Successfully minimized 99th percentile of control effort in aerocapture mission

Validated the approach with a Gaussian random field disturbance model

Demonstrated effective covariance control under spatial uncertainties

Abstract

The problem of optimizing affine feedback laws that explicitly steer the mean and covariance of an uncertain system state in the presence of a Gaussian random field is considered. Spatially-dependent disturbances are successively approximated with respect to a nominal trajectory by a sequence of jointly Gaussian random vectors. Sequential updates to the nominal control inputs are computed via convex optimization that includes the effect of affine state feedback, the perturbing effects of spatial disturbances, and chance constraints on the closed-loop state and control. The developed method is applied to solve for an affine feedback law to minimize the 99th percentile of $\Delta v$ required to complete an aerocapture mission around a planet with a randomly disturbed atmosphere.