🤖 AI Summary
This work addresses the challenges of model inaccuracy and ambiguous state distributions in nonlinear systems by proposing a distributionally robust optimization-based chance-constrained control framework. The approach constructs an ambiguity set using relative entropy constraints and derives an upper bound on risk expectations via the variational representation of the exponential integral. It further integrates nonlinear covariance propagation with adaptive determination of the ambiguity set radius based on second-order dynamic truncation error. Notably, the method recovers nominal risk in the zero-divergence limit, thereby overcoming the restrictive assumptions of Gaussianity prevalent in conventional approaches. Validation on spacecraft stochastic guidance tasks demonstrates that the proposed framework effectively enforces probabilistic safety constraints under distributional uncertainty.
📝 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.