The fifth generation (5G) mobile communications systems promises very high bitrates and ultra-low latencies, whilst at the same time hosting a massive amount of edge computing power. These 5G qualities are expected to spur a multitude of services such as broadband access in dense areas, augmented and virtual reality, extreme real-time and ultra-reliable communications, among others. However, an effective control of such communication and computation tasks is extremely challenging due to its real-time nature. With this project, we target the development of pioneering mathematical and algorithmic tools for the real-time control of radio access and computation resources in 5G mobile networks. To effectively tackle this, we have united an interdisciplinary team, featuring highly reputed young professionals in telecommunications, control theory and computer science. The main project outcomes are: a predictive, distributed, and asynchronous optimization framework, with stability guarantees, and an open source large scale simulator, to quantify the effectiveness of the developed solutions. A smooth and effective integration of theory, algorithms and simulation software will be ensured by a sensible secondment plan involving the hired young researchers.