The modelling of quantum control systems

High-performance control of quantum dynamics is key to the development of quantum technologies. From quantum-state engineering to quantum metrology, theory and practice of quantum control enable robust and cheaper technologies for future industrial applications. Starting from fundamental matter-field interactions, we overview various approaches to modelling quantum control systems, in which control can be implemented by either changing field or material properties. These models are built in time or frequency domain and can be interconnected to form quantum feedback networks. This review can be taken as a useful reference for engineers to understand the quantum physics behind, or for physicists to resolve control problems from a control engineering point of view.