A Composition Operator for Systems with Active and Passive Actions

We investigate requirements for a composition operator for complex control systems. The operator should be suitable for a context where we have both supervisory control and a system that consists of multiple (two or more) components. We conclude that using both passive (observing) and active (controlling) transitions is advantageous for the specification of supervisory control systems. We introduce a composition operator that meets the requirements. We give both operational and trace semantics for this operator and give necessary and sufficient conditions for commutativity and associativity.