We propose novel methods for modelling, analysis and control of complex, large scale systems. Fundamental research is motivated by applied problems in power networks. We adopt the framework of stochastic hybrid systems (SHS), which allows one to capture the interaction between continuous dynamics, discrete dynamics and probabilistic uncertainty. In the context of power networks, SHS arise naturally: continuous dynamics model the evolution of voltages, frequencies, etc. discrete dynamics changes in network topology, and probability the uncertainty about power demand and (with the advent of renewables) power supply. More generally, because of their versatility, SHS are recognized as an ideal framework for capturing the intricacies of complex, large scale systems. Motivated by this, considerable research effort has been devoted to the development of modelling, analysis and control methods for SHS, in computer science (giving rise to theorem proving and model checking methods) and in control engineering (giving rise to optimal control and randomized methods). Despite several success stories, however, none of the methods currently available are powerful enough to deal with real life large scale applications. We feel that a key reason for this is that the methods have been developed by different communities in relative isolation, motivated by different applications. As a consequence synergies between them have never been fully explored. We propose to systematically exploit such synergies. Our multi-disciplinary team, which brings together experts on all the state of the art SHS methods, will establish links between model checking, theorem proving, optimal control and randomized methods. Leveraging on their complementary strengths we will develop combined strategies and tools to enable novel applications to complex, large scale systems. Common power networks case studies will provide a testing ground for the fundamental developments, motivate them, and keep them focused.