Aydin Aybar

Overlapping decompositions and expansions of Petri nets

Overlapping decompositions and expansions are considered to design decentralized controllers for discrete-event systems (DESs) modeled by Petri nets. The inclusion principle for Petri nets is first defined. It is shown that properties like boundedness, reversibility, and liveness (with a mild additional condition) carry over from the including net to the included net. Moreover, a new property called obstruction, is introduced for the including net, and it is shown that if obstruction does not occur in the including net, then deadlock does not occur in the included net. An expansion procedure, which guarantees inclusion for an overlappingly decomposed Petri net, is then introduced.

Centralized and decentralized supervisory controller design to enforce boundedness, liveness, and reversibility in Petri nets

Supervisory controller design to enforce boundedness, liveness, and reversibility in Petri nets is considered. The Petri nets considered may have non-unity weight arcs and both controllable and uncontrollable transitions. Algorithms for a centralized controller design approach are first developed. The developed algorithms always find a controller whenever it exists. This controller enforces boundedness, liveness, and reversibility; it also avoids deadlock. Furthermore, it is shown that the controller obtained is the least restrictive controller among all controllers which enforce desired properties. A decentralized controller design approach, based on overlapping decompositions, is then introduced. Algorithms to design decentralized controllers based on this approach are also developed. These controllers, when they exist, also guarantees boundedness, liveness, reversibility and deadlock freeness. The decentralized controllers have two main advantages over the centralized ones. First, they have reduced on-line computation and communication requirements. Second, the computational time required to design decentralized controllers is considerably less than that required for centralized controllers.

Deadlock Avoidance Controller Design for Timed Petri Nets Using Stretching

The recently introduced method, which was called ldquostretching,rdquo is extended to timed Petri nets which may have both controllable and uncontrollable transitions. Using this method, a new Petri net, called ldquostretched Petri net,rdquo which has only unit firing durations, is obtained to represent a timed-transition Petri net. Using this net, the state of the original timed Petri net can be represented easily. This representation also makes it easy to design a supervisory controller for a timed Petri net for any purpose. In this paper, supervisory controller design to avoid deadlock is considered in particular. Using this method, a controller is first designed for the stretched Petri net. Then, using this controller, a controller for the original timed Petri net is obtained. Algorithms to construct the reachability sets of the stretched and original timed Petri nets, as well as algorithms to obtain the controller for the original timed Petri net are presented. These algorithms are implemented using Matlab. Examples are also presented to illustrate the introduced approach.

Decentralized supervisory controller design to avoid deadlock in Petri nets

A decentralized supervisory controller design approach, using overlapping decompositions, is proposed for discrete-event systems modelled by Petri nets to avoid deadlock. In this approach, the given original Petri net is first decomposed into overlapping Petri subnets. A controller for each disjoint Petri subnet is then designed. A controller for the expanded Petri net is next obtained by combining these controllers in a certain way. In the final phase, the controller obtained for the expanded Petri net is contracted in a certain way to obtain a controller for the original Petri net. It is proved that this final controller avoids deadlock in the original Petri net.

Controller Design to Enforce Boundedness, Liveness, and Reversibility in Petri Nets 1

Abstract Supervisory controller design to enforce boundedness, reversibility, and liveness in ordinary Petri nets with weighted arcs is considered. Algorithms are presented to design a controller to enforce these properties simultaneously. It is shown that the proposed approach always finds a controller to enforce these properties whenever it is possible. Furthermore, the controller obtained is the least restrictive controller among all controllers which enforce these properties simultaneously.

OVERLAPPING DECOMPOSITIONS OF LARGE–SCALE DISCRETE–EVENT SYSTEMS

Abstract Overlapping decompositions and expansions of discrete–event systems (DESs) modeled by automata or formal languages are considered. Inclusion principle for such systems is defined. A decentralized supervisory controller design approach is then introduced. To apply the proposed approach, the automaton of the given DES is first decomposed overlappingly and expanded to obtain disjoint subautomata. A controller is then designed for each disjoint subautomaton. These controllers are then combined to obtain a controller for the expanded DES. In the final phase, a controller for the original DES is obtained from the controller determined for the expanded DES. It is shown that, for large–scale DESs, the proposed approach requires very little computation to design a controller compared to a centralized design approach.

Decentralized Control Design for Interconnected Discrete-Event Systems

Abstract Interconnected discrete event, systems are studied in this paper. Petri nets are used to model these systems. A decentralized controller design approach, based on overlapping decompositions, is described for such systems. A manufacturing system example is also presented

Representation of the State of Timed-Place Petri Nets Using Stretching

Abstract Unlike untimed Petri nets, representation of the state of a timed Petri net and describing its evolution is not an easy task. Here, an approach, called place-stretching , is introduced to represent the state of a timed-place Petri net. This approach also facilitates the description of the evolution of the state of a timed-place Petri net. An algorithm, which uses this approach, to construct the reachability set of a timed-place Petri net is also developed. An example is also presented to demonstrate the introduced approach and the usage of the developed algorithm.

Line estimation for a line-following mobile robot

In this study, the coordinate of the line position for a differential drive line-following mobile robot is estimated by using the Minimum Variance Unbiased Estimator. Using the sensor data as an observation data and coordinates of sensors, a linear model for Minimum Variance Unbiased Estimator is constructed. MATLAB simulations for computing Root-Mean-Square-Error and Monte Carlo Simulations and real world data are used to analyze the performance of the estimator. Using the estimated value, a feedback for PID controller is used to compute deviation in order to make the mobile robot follow the line.

Corrections to 'Decentralized supervisory controller design to avoid deadlock in Petri nets'

Furthermore, for any transition, t, in the overlapping part of two PSNs, any element of UTðtÞ :1⁄4 fp 2 P j Oðp; tÞ 1⁄4 1g and of VT ðtÞ :1⁄4 fp 2 P j Nðp; tÞ 1⁄4 1g must also be in the overlapping part of the same two PSNs. Moreover, here we also require that any transition in any overlapping part should be controllable and that, for any place, p, in any overlapping part we must have UPðpÞ :1⁄4 ft 2 T j Nðp; tÞ 1⁄4 1g Tc. Also, in line 8 of the second paragraph of proof of Theorem 2 (fourth paragraph of the second column on page 1288), ‘Since no ~ t 2 ~ T can fire’ should be replaced by ‘Since no ~ t 2 T can fire’.