Relative Entropy-Bounded Ambiguous Chance Constraints for Robust Planning in Nonlinear Systems

• URL: http://arxiv.org/abs/2607.16977v1
• Date: Sat, 18 Jul 2026 22:02:52 GMT
• Title: Relative Entropy-Bounded Ambiguous Chance Constraints for Robust Planning in Nonlinear Systems
• Abstract summary: Current approaches for chance-constrained control assume that the true state distribution is known and distributed.<n>In this work, we define a distribution ambiguity set and, with a variational expression for exponential integrals, bound the expected risk value under an unknown distribution.<n>Our bound recovers the reference risk value in the zero-divergence limit.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider defining risk probability in stochastic control problems under distribution ambiguity. Current approaches for chance-constrained control typically assume that the true state distribution is known and Gaussian distributed. These assumptions are not amenable to many real-world engineering applications where system dynamics are nonlinear and only approximately modeled. In this work, we define a distribution ambiguity set and, with a variational expression for exponential integrals, bound the expected risk value under an unknown distribution that resides within a relative entropy distance of a nominal Gaussian reference distribution. Our bound recovers the reference risk value in the zero-divergence limit. A method is presented to determine the relative entropy distance defining the ambiguity set that is a function of the reference covariance evolution and second-order dynamical truncation errors. The resulting contributions provide a framework for handling distributional ambiguity in nonlinear covariance steering problems. A stochastic spacecraft guidance example is presented to demonstrate our contributions.

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