An Optimization Approach to Petri Net Monitor Design

Abstract

This paper addresses the problem of enforcing generalized mutual exclusion constraints on a Petri net plant. Firstly, we replace the classical partition of the event set into controllable and uncontrollable events from supervisory control theory, by associating a control and observation cost to each event. This leads naturally to formulate the supervisory control problem as an optimal control problem. Monitor places which enforce the constraint are devised as a solution of an integer linear programming problem whose objective function is expressed in terms of the introduced costs. Secondly, we consider timed models for which the monitor choice may lead to performance optimization. If the plant net belongs to the class of mono-T-semiflow nets, we present an integer linear fractional programming approach to synthesize the optimal monitor so as to minimize the cycle time lower bound of the closed loop net. For strongly connected marked graphs the cycle time of the closed loop net can be minimized.

An optimization approach towards improved Petri net monitor design

“…Consequently, a supervisor with the least implementation cost can be synthesized through a set of IP formulations. In this paper, we show through a few examples that the approach in [3] may lead to paradoxical results in some cases. As a result, despite its significance for supervisory control, its applicability is limited without proper modification.…”

“…This method always results in a more restrictive but safer monitor. To further generalize the approach in the same vein, each transition is associated with an observation and control cost in [3]. Consequently, a supervisor with the least implementation cost can be synthesized through a set of IP formulations.…”

“…In the consecutive sections, basic notations of Petri nets are given. The problem of the algorithm in [3] is illustrated through a few explanatory examples. The mechanisms that cause the mentioned problems are discussed.…”

An Enhanced Supervisory Control Strategy for Periodicity Mutual Exclusions in Discrete Event Systems Based on Petri Nets

“…Such a specification consists of a disjunction of conjunction of several single generalized mutual exclusion constraints. The authors in [42] enforce the generalized mutual exclusion constraints on a Petri net plant by replacing the classical partition of event set into controllable and uncontrollable events from supervisory control theory. In [43], an algorithm is presented to transform a given generalized mutual exclusion constraint into an optimal admissible one for a class of Petri nets whose uncontrollable influence subnets are forward synchronization and backward conflict-free nets.…”

Online Fault Diagnoser for Partially Observed Petri Nets

“…The Petri Nets (PN) model offers a twofold representation: rigorous mathematical foundation and intuitive graphical representation, so the Petri Nets model is widely used in the DES [9][10] [13] [14][15][16]. Fault detection and diagnosis methods for the DES based on Petri Nets in current research mainly includes P-invariants [1], the basic reachability graph (BRG) [8], labeled PN [11], the compiled diagnoser [4], the interpreted diagnoser [3], the unfolding approach, integer linear programming (ILP) method [12], and so on.…”