Controllability of Weakly Dependent Siphons under Elementary-Siphon Control

Monitors are added upon problematic siphons to avoid deadlocks. Li and Zhou add monitors to elementary siphons only while controlling the rest dependent siphons to save cost. After failing a Marking Linear Inequality (MLI) test, they perform a Linear Integer Programming (LIP) test (NP-hard). We proposed a new MLI test earlier to avoid the LIP and extended it to S3PGR2 (systems of simple sequential processes with general resource requirements) for strongly dependent siphons (SDS). The control policy for weakly dependent siphons (WDS) is rather conservative due to some negative terms in the MLI. This paper shows that WDS and SDS have the same controllability (i.e., MLI). As a result, the control for WDS needs no longer be that conservative. We also develop an optimization (by redundancy elimination) of the computation required for LIP test to ensure deadlock prevention of S3PR (Systems of Simple Sequential Processes with Resources). A favorable result for this policy is that any n-dependent (n>2) WDS (similar to SDS) needs no monitor and hence the complexity for synthesizing a controller becomes polynomial.

Design of Optimized Petri Net Supervisors for Flexible Manufacture Systems Based on Elementary Siphons

This chapter focuses on the deadlock prevention problems in Flexible Manufacturing Systems (FMS), and the major target is to design more excellent controllers that lead to a more permissive supervisor by adding a smaller number of monitors and arcs than the existing ones in the literature for the design of liveness-enforcing Petri net supervisors. The authors distinguish siphons in a Petri net model by elementary and dependent ones. For each elementary siphon, a monitor is added to the plant model such that it is invariant-controlled without generating emptiable control-induced siphons, and the controllability of a dependent siphon is ensured by changing the control depth variables of its related elementary siphons. Hence, a structurally simple Petri net supervisor is achieved. Based on the previous work, this chapter explores two optimized deadlock prevention approaches based on elementary siphons that can achieve the same control purpose and have more excellent performance.