Incremental and Hierarchical Deadlock-Free Control of Discrete Event Systems with Variables
In this report, we present an incremental and hierarchical deadlock-free control architecture for discrete event systems with variables. Given a system including several components that share alphabet and variables, we first introduce partial controllers that only control parts of each component that have local control behavior w.r.t. other components, and leave other parts intact. This enables us to compute a maximally permissive (or optimal) controller for the given system in an incremental way, rather than on the entire system at once.
Second, to leverage the hierarchical supervisory control approach for systems with no variables using natural projections with observer and local control consistency (LCC) properties, we lift these concepts to systems with variables by introducing a new variable-observer condition. We show that these conditions are sufficient enough for optimal hierarchical control. Furthermore, similar to the observer condition and the LCC, we formulate the variable-observer condition in terms of a quasi-congruence. An industrial manufacturing example demonstrates the computational effectiveness and practical usage of the proposed control architecture.