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

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. Spatiallydependent 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 99 th percentile of Δ𝑣 required to complete an aerocapture mission around a planet with a randomly disturbed atmosphere.