The Relation between the Virtual Actuator and the Dual Observer

This article compares the virtual actuator and the dual observer, which represent two feedback systems for controlling linear systems that have been developed in different contexts. Both systems are dual to state observers. It is shown that the virtual actuator, which was recently developed for the purpose of fault-tolerant control, is a generalisation of the dual observer, which was proposed several decades ago as a means to realise output injection control. This result is obtained by considering a special case of the virtual actuator that establishes identity between the dual observer and the virtual actuator, and it opens new fields of applications for virtual actuators beyond the domain of fault-tolerant control.