DeSKO: Stability-Assured Robust Control with a Deep Stochastic Koopman Operator

Koopman operator theory linearly describes nonlinear dynamical systems in high-dimensional functional space, this facilitates the application of linear control methods to nonlinear systems. However, the Koopman operator does not account for uncertainty in dynamical systems, leading to fragile control performance in real-world applications. We propose using a deep stochastic Koopman operator (DeSKO) model in a robust learning control framework to guarantee stability. The DeSKO model can learn the uncertainty contained in the dynamical system and infer a distribution of observables. We use the inferred distribution to design a robust and stabilizing closed-loop controller for the dynamical system. Modeling and control experiments show that our presented framework is more robust and scalable than state-of-art deep Koopman operators and reinforcement learning methods on several advanced control benchmarks, including a soft robotic arm, a legged robot, and a biological gene regulatory network. Furthermore, we demonstrate that this method resists previously unseen uncertainties, such as external disturbances, with a magnitude of up to five times the maximum control input. Our approach opens up new possibilities in robustly managing internal or external uncertainty while controlling high-dimensional nonlinear systems in a learning framework.