On the Problem of Reformulating Systems with Uncertain Dynamics as a Stochastic Differential Equation
This addresses a methodological issue in control theory for researchers, but it is incremental as it critiques existing approaches without proposing a new solution.
The paper identifies a problem in recent learning-based control approaches that reformulate systems with uncertain dynamics as stochastic differential equations, specifically critiquing the approximation of epistemic uncertainty as aleatoric uncertainty.
We identify an issue in recent approaches to learning-based control that reformulate systems with uncertain dynamics using a stochastic differential equation. Specifically, we discuss the approximation that replaces a model with fixed but uncertain parameters (a source of epistemic uncertainty) with a model subject to external disturbances modeled as a Brownian motion (corresponding to aleatoric uncertainty).