Synthesis Method for Hierarchical Interface-based Supervisory Control

Abstract

Hierarchical Interface-Based Supervisory Control (HISC) decomposes a discrete-event system (DES) into a high-level subsystem which communicates with n ≥ 1 low-level subsystems, through separate interfaces. It provides a set of local conditions that can be used to verify global conditions such as nonblocking and controllability such that the complete system model never needs to be constructed.Currently, a designer must create the supervisors himself and then verify that they satisfy the HISC conditions. In this paper, we develop a synthesis method that can take advantage of the HISC structure.We replace the supervisor for each level by a corresponding specification DES. We then construct for each level a maximally permissive supervisor that satisfies the corresponding HISC conditions.We define a set of language based fixpoint operators and show that they compute the required level-wise supremal languages. We then discuss the complexity of our algorithms and show that they potentially offer significant savings over the monolithic approach. We also briefly discuss a symbolic HISC verification and synthesis method using Binary Decision Diagrams, that we have also developed.A large manufacturing system example (worst case state space on the order of 10 30 ) extended from the AIP example is briefly discussed. The example showed that we can now handle a given level with a statespace as large as 10 15 states, using less than 160MB of memory. This represents a significant improvement in the size of systems that can be handled by the HISC approach. A software tool for synthesis and verification of HISC systems using our approach was also developed.

Hierarchical interface-based supervisory control with data events

“…46th IEEE CDC, New Orleans, USA, Dec. [12][13][14]2007 FrC04.2 In order to restrict information flow and decouple the subsystems, the system alphabet is partitioned into pairwise disjoint alphabets:…”

“…To these two event types present in the HISC formulation of [1], [2], [3], [4], we add a new event type called low data events. These events provide a means for a low-level to send information (data) through the interface, independent of the standard command-answer structure offered by the request and answer events.…”

“…We will then present our nonblocking and controllability results. Next we will discuss how to use the new method to model buffers, followed by an application to the AIP example from [1], [4].…”

Modular requirements for Hierarchical Interface-Based Supervisory Control with multiple levels

“…Proof of Theorem 3 can be found in [12] and follows closely the logic presented in [13], where the only difference is that the interface consistency requirement has been relaxed. Specifically, Point 4 of Definition 4 has been modified from what was originally a controllability requirement to the reachability requirement prescribed in this paper.…”

“…Likewise, the request event r 2 can be reached from state 4 via low-level events. Point 4 of the interface consistency definition is specifically employed in Proposition 13 of [13]. A revised version of this proposition using the modified Point 4 can be found in [12].…”