Supervisory control of extended finite automata using transition projection

Abstract

Abstract-A limitation of the Ramadge and Wonham (RW) framework for the supervisory control theory is the explicit state representation using finite automata, often resulting in complex and unintelligible models. Extended finite automata (EFAs), i.e., deterministic finite automata extended with variables, provide compact state representation and then make the control logic transparent through logic expressions of the variables. A challenge with this new control framework is to exploit the rich control structure established in RW's framework. This paper studies the decentralized control structure with EFAs. To reduce the computational complexity, the controller is synthesized based on model abstraction of subsystems, which means that the global model of the entire system is unnecessary. Sufficient conditions are presented to that guarantee the decentralized supervisors result in maximally permissive and nonblocking control to the entire system.

Abstractions for nonblocking supervisory control of Extended Finite Automata

“…Proof: See [24]. The extension to an arbitrary number of synchronized factors is straightforward and is left out.…”

“…Proof: See [24]. As we establish a "reliable interface" for EFAs by introducing E-observer, the interaction between two complex systems may be examined through their projections rather than their global behavior.…”