Existing modeling and control methods for real-world systems typically deal with uncertainty and nonlinearity on a case-by-case basis. We present a universal and robust control framework for the general class of uncertain nonlinear systems. Our data-driven deep stochastic Koopman operator (DeSKO) model and robust learning control framework guarantee robust stability. DeSKO learns the uncertainty of dynamical systems by inferring a distribution of observables. The inferred distribution is used in our robust and stabilizing closed-loop controller for dynamical systems. We also develop a model predictive control framework with integral action to compensate for run-time parametric uncertainty, such as manipulating unknown objects. Modeling and control experiments in simulation show that our presented framework is more robust and scalable for robotic systems than state-of-the-art controllers using deep Koopman operators and reinforcement learning (RL) methods. We demonstrate that our method resists previously unseen uncertainties, such as external disturbances, at a magnitude of up to five times the maximum control input. Furthermore, we test our DeSKO-based control framework on a real-world soft robotic arm. It shows that our framework outperforms model-based controllers that have full knowledge of the model parameters, and the controller can conduct object pick-and-place tasks without further training. Our approach opens up new possibilities in robustly managing internal or external uncertainty while controlling high-dimensional nonlinear systems in a learning framework. This approach serves as a foundation to greatly simplify high-level control and decision-making for robots.

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.