Recent work in the area of interdependent networks has focused on interactions between two systems of the same type. However, an important and ubiquitous class of systems are those involving monitoring and control, an example of interdependence between processes that are very different. In this Article, we introduce a framework for modelling distributed supervisory control in the guise of an electrical network supervised by a distributed system of control devices. The system is characterised by degrees of freedom salient to real-world systems--- namely, the number of control devices, their inherent reliability, and the topology of the control network. Surprisingly, the behavior of the system depends crucially on the reliability of control devices. When devices are completely reliable, cascade sizes are percolation controlled; the number of devices being the relevant parameter. For unreliable devices, the topology of the control network is important and can dramatically reduce the resilience of the system.