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

The Koopman operator theory linearly describes nonlinear dynamical systems in a high-dimensional functional space and it allows to apply linear control methods to highly nonlinear systems. However, the Koopman operator does not account for any uncertainty in dynamical systems, causing it to perform poorly in real-world applications.Therefore, we propose a deep stochastic Koopman operator (DeSKO) model in a robust learning control framework to guarantee stability of nonlinear stochastic systems. The DeSKO model captures a dynamical system's uncertainty by inferring a distribution of observables. We use the inferred distribution to design a robust, stabilizing closed-loop controller for a dynamical system. Modeling and control experiments on several advanced control benchmarks show that our framework is more robust and scalable than state-of-the-art deep Koopman operators and reinforcement learning methods. Tested control benchmarks include a soft robotic arm, a legged robot, and a biological gene regulatory network. We also demonstrate that this robust control 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 learning control for high-dimensional nonlinear systems while robustly managing internal or external uncertainty.