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

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.

Optimization and Control (math.OC); Information Theory (cs.IT); Robotics (cs.RO)

arXiv:2607.16977 [math.OC]

(or arXiv:2607.16977v1 [math.OC] for this version)

https://doi.org/10.48550/arXiv.2607.16977 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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