Approximate Relative Entropy Constraints for Nonlinear Covariance Steering Under Distribution Ambiguity

• URL: http://arxiv.org/abs/2607.16914v1
• Date: Sat, 18 Jul 2026 18:09:59 GMT
• Title: Approximate Relative Entropy Constraints for Nonlinear Covariance Steering Under Distribution Ambiguity
• Abstract summary: Covariance steering provides an efficient framework for designing linear feedback policies.<n>Risk-sensitive quantities such as collision probability and mean-squared error may be inaccurately estimated.<n>This work develops a distributionally robust covariance-steering framework based on the relative entropy.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Covariance steering provides an efficient framework for designing linear stochastic feedback policies, but its extension to nonlinear systems relies on a Gaussian surrogate obtained through local linearization. Because this surrogate may differ substantially from the true nonlinear state distribution, risk-sensitive quantities such as collision probability and mean-squared error may be inaccurately estimated. This work develops a distributionally robust covariance-steering framework based on the relative entropy, also known as the Kullback-Leibler divergence (KLD), to account for ambiguity in the propagated probability density function. Using a variational representation of exponential integrals, we derive computable upper bounds on risk-sensitive quantities over a KLD ambiguity set. We then formulate an upper bound on the time rate of change of the KLD between the true nonlinear distribution and a Gaussian reference surrogate. Under some assumptions, this bound is controlled by decision variables within a covariance-steering formulation. The resulting constraints are incorporated into a sequential convex programming algorithm to design stochastic guidance policies that keep the true distribution close to its Gaussian surrogate while enforcing bounds on risk-sensitive performance measures. The proposed approach is demonstrated on a challenging nonlinear spacecraft transfer between two near-rectilinear halo orbits.

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