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

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.