I will develop efficient on-line control methods for large-scale Networks with Hybrid Dynamics (NHDs) in the presence of uncertainties, where hybrid dynamics refers to a combination of continuous dynamics, mode switches, and/or topology changes. This topic is one of the core fundamental open problems in the field of systems and control. It is also important from a societal point of view as today’s society depends heavily on the reliable and efficient operation of road, railway, electricity, gas, and water networks, all of which are examples of large-scale NHDs.<br/><br/>Control of large-scale NHDs is a very complex problem due to the large size of the networks, the presence of disturbances, and the hybrid dynamics, while a limited computation time is available. State-of-the-art control methods are not suited for large-scale NHDs as they either suffer from computational tractability issues or impose additional restrictions, resulting in a significantly reduced performance.<br/><br/>To address this problem, I will create a new on-line control paradigm for large-scale NHDs based on an innovative integration of multi-agent optimization-based and learning-based control, allowing to unite the optimality of optimization-based control with the on-line tractability of learning-based control. I will bridge the gap between optimization-based and learning-based control for NHDs through the use of multi-scale multi-resolution piecewise affine models, explicit consideration of the graph structure of the network, the unique knowledge and experience I have in both optimization-based control and learning-based decision making, and an interdisciplinary integration of approaches from systems and control, computer science, and optimization.<br/><br/>This will result in systematic, very reliable, highly scalable, high-performance on-line control methods for large-scale NHDs. I will demonstrate their feasibility, benefits, and impact for green multi-modal transportation networks and smart multi-energy networks.