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Soft grippers are gaining momentum across applications due to their flexibility and dexterity. However, the infinite-dimensionality and non-linearity associated with soft robots challenge modeling and closed-loop control of soft grippers to perform grasping tasks. To solve this problem, data-driven methods have been proposed. Most data-driven methods rely on intensive model learning in simulation or offline, and as such it may be hard to generalize across different settings not explicitly trained upon and in physical robot testing where online control is required. In this paper, we propose an online modeling and control algorithm that utilizes Koopman operator theory to update an estimated model of the underlying dynamics at each time step in real-time. The learned and continuously updated models are then embedded into an online Model Predictive Control (MPC) structure and deployed onto soft multi-fingered robotic grippers. To evaluate the performance, the prediction accuracy of our approach is first compared against other model-extraction methods among different datasets. Next, the online modeling and control algorithm is tested experimentally with a soft 3-fingered gripper grasping objects of various shapes and weights unknown to the controller initially. Results indicate a high success ratio in grasping different objects using the proposed method. Sample trials can be viewed at https://youtu.be/i2hCMX7zSKQ.