Relative Entropy-Bounded Ambiguous Chance Constraints for Robust Planning in Nonlinear Systems
Information TheoryRobotics
Summary
The authors study how to handle uncertainty in the probability of risk when controlling systems with unpredictable behavior, especially when the exact state distribution is unknown or not Gaussian. They create a way to define a set of possible distributions near a known Gaussian distribution, using a measure called relative entropy to handle ambiguity. They also show how to calculate a bound on risk values that works even when the true distribution is different but similar to the Gaussian reference. Their approach is applied to a spacecraft guidance problem to demonstrate its usefulness in nonlinear control scenarios.
Authors
Trevor N. Wolf, Jay W. McMahon
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.