This paper demonstrates the benefits of imposing stability on data-driven Koopman operators. The data-driven identification of stable Koopman operators (DISKO) is implemented using an algorithm \cite{mamakoukas_stableLDS2020} that computes the nearest \textit{stable} matrix solution to a least-squares reconstruction error. As a first result, we derive a formula that describes the prediction error of Koopman representations for an arbitrary number of time steps, and which shows that stability constraints can improve the predictive accuracy over long horizons. As a second result, we determine formal conditions on basis functions of Koopman operators needed to satisfy the stability properties of an underlying nonlinear system. As a third result, we derive formal conditions for constructing Lyapunov functions for nonlinear systems out of stable data-driven Koopman operators, which we use to verify stabilizing control from data. Lastly, we demonstrate the benefits of DISKO in prediction and control with simulations using a pendulum and a quadrotor and experiments with a pusher-slider system. The paper is complemented with a video: \url{https://sites.google.com/view/learning-stable-koopman}.
Jerk Control of Floating Base Systems with Contact-Stable Parametrised Force Feedback
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Dynamic Interaction Control, Istituto Italiano di Tecnologia（意大利理工学院动态交互控制实验室）；DIBRIS, University of Genova（热那亚大学 DIBRIS）
Research on Stable Obstacle Avoidance Control Strategy for Tracked Intelligent Transportation Vehicles in Non-structural Environment Based on Deep Learning
Learning Stable Robot Grasping with Transformer-based Tactile Control Policies
Italian Institute of Technology（意大利技术研究院）；University of Genoa（热那亚大学）；National University of Singapore（新加坡国立大学）；Institute for Infocomm Research (IR), A*STAR（新加坡科技研究局信息通信研究所）；King’s College London（伦敦国王学院）
