Asma Ghaffari

Design of a live and maximally permissive Petri net controller using the theory of regions

This paper addresses the forbidden state problem of Petri nets (PN) with liveness requirement and uncontrollable transitions. The proposed approach computes a maximally permissive PN controller, whenever such a controller exists. The first step, based on a Ramadge-Wonham-like reasoning (1989), determines the legal and live maximal behavior the controlled PN should have. In the second step, the theory of regions is used to design control places to add to the original model to realize the desired behavior. Furthermore, necessary and sufficient conditions for the existence of control places realizing the maximum permissive control are given. A parameterized manufacturing application of significant state space is used to show the efficiency of the proposed approach.

Live and Maximally Permissive Controller Synthesis Using Theory of Regions

This paper addresses the forbidden state problem of Petri nets with liveness requirement and uncontrollable transitions. The proposed approach synthesizes in two steps an optimal Petri net-based controller, whenever such a controller exists. First, the behavior of the closed loop system is computed with a Ramadge-Wonham-like approach. Then, control places, that realize the computed behavior when added to the original model, are synthesized. Necessary and sufficient condition of the existence of such places is obtained. A manufacturing application of the method shows its efficiency.

Design and coordination of partial petri net controllers for a maximally permissive supervisory control

In a previous work, we proposed a general approach for synthesizing a maximally permissive Petri net controller as a set of control places to connect to a given plant Petri net model. The resulting net has the maximum behavior w.r.t. forbidden state specifications. However, Petri net controller does not always exist. Such situations are geometrically caracterized and a solution is proposed in this paper for forbidden state problems for which no Petri net controller exists. It is shown that a maximally permissive control policy may be achieved by accounting of the actions of several partial Petri net controllers. Each of them prevents the reachability of at least one forbidden state transition and allows any marking in the desired behavior. The design procedure of partial PN controllers detailed here is based on the approach we previously proposed. It is applied to an example.

Maximally permissive and non-blocking control of Petri nets using theory of regions

Forbidden state problem of Petri nets with non-blocking requirement and uncontrollable transitions is addressed in this paper. The approach proposed in this paper combines the Ramadge-Wonhams (1989) approach and the theory of regions, a theory recently proposed for compiling a labelled automaton into a Petri net. It first determines the automaton model of the closed loop system using a Ramadge-Wonham-like approach. It then uses the theory of regions to design a set of control places to add to the initial Petri net to realize the maximum permissive and non-blocking control. Although the proposed approach does not avoid the state explosion problem in its design phase, it does provide a compact representation of the optimum control in terms of control places and hence can be very useful in the implementation of optimum control.

NET TRANSFORMATION AND THEORY OF REGIONS FOR OPTIMAL SUPERVISORY CONTROL OF PETRI NETS

Abstract In a previous work, we applied the theory of regions to design optimal Petri net controller by adding so-called control places to the plant Petri net model with uncontrolable transitions and forbidden states. Unfortunately, such a simple control-place-based solution does not always exist. In the present paper, we propose a new approach for designing optimal controller for ordinary bounded Petri nets using control places. The key idea consists in transforming the plant Petri net model, for which a control-place-based solution was not found, into a safe Petri net. Then, exploiting the result stating that forbidden state problems of safe Petri nets always have control-place-based solutions, the control problem of the transformed model is optimally solved using our previous result. Besides, by assigning a priority to transitions of the transformed model, the complexity is considerably reduced.

State feedback control of discrete event systems using marked graphs

Addresses the state feedback control of marked graphs with uncontrollable transitions and forbidden states. Control requirements are expressed as the conjunction of general mutual exclusion constraints (GMEC) of markings of so-called critical places. Structural properties such as influence paths and influence zones are defined to perform the worst-case analysis for each GMEC specification with any given initial marking when only uncontrollable transitions are allowed. A simple analytical solution of the maximal uncontrollably reachable marking of any critical place is proposed. It is then extended to paths of critical places. We further distinguish the case where critical places are independent. We prove that the worst-case marking of a GMEC specification of independent critical places corresponds to the worst-case marking of each critical place.