Ali A. Afzalian

Vahid Saeidi, Ali A. Afzalian, Davood Gharavian

Decomposition and localization of a supervisor both are reduction methods in distributed supervisory control of discrete-event systems.Decomposition is employed to reduce the number of events and localization is used to reduce the number of states of local controllers.In decomposition of a supervisor both observation and control scopes are restricted, whereas in localization only control authority is restricted to the corresponding local controller. In this paper, we propose a decomposition method by defining coparanormality property, and by using relative observability property of a monolithic supervisor. Coparanormality is a coobservation property defined based on paranormality property for a set of natural projections.It is shown that each supervisor can be coparanormal, provided a set of appropriate natural projections exist. Moreover, it is proved that relative observability is a sufficient condition for decomposition of a supervisor. Furthermore, the supervisor localization procedure is generalized to find a set of local controllers for any partition ofthe controllable events set. The implementation of such local controllers may become easier in industrial systems.

Vahid Saeidi, Ali A. Afzalian, Davood Gharavian

Supervisory control synthesis encounters with computational complexity. This can be reduced by decentralized supervisory control approach. In this paper, we define intrinsic control consistency for a pair of states of the plant. G-control consistency (GCC) is another concept which is defined for a natural projection w.r.t. the plant. We prove that, if a natural projection is output control consistent for the closed language of the plant, and is a natural observer for the marked language of the plant, then it is G-control consistent. Namely, we relax the conditions for synthesis the optimal non-blocking decentralized supervisory control by substituting GCC property for L-OCC and Lm-observer properties of a natural projection. We propose a method to synthesize the optimal non-blocking decentralized supervisory control based on GCC property for a natural projection. In fact, we change the approach from language-based properties of a natural projection to DES-based property by defining GCC property.

Vahid Saeidi, Ali A. Afzalian, Davood Gharavian

Supervisor localization procedure can be employed to construct local controllers corresponding to component agents in discrete-event systems. The proposed method in [11] is based on state reduction of a monolithic supervisor with respect to each set of controllable events corresponding to each component agent. A supervisor is localizable if state cardinality can be reduced from the reduced supervisor to each local controller. Although event reduction is an important property, the original supervisor localization procedure did not guarantee event reduction in each local controller comparing to the reduced supervisor. In this paper, we propose a method to localize a supervisor with event reduction in each local controller comparing to the reduced supervisor. State reduction facilitates the implementation of local controllers on industrial systems, whereas event reduction reduces communication traffic between each pair of local controllers.

Vahid Saeidi, Ali A. Afzalian, Davood Gharavian

Supervisor reduction procedure can be used to construct the reduced supervisor with a reduced number of states in discrete-event systems. The main concepts which are used in this procedure are control consistency of states, control cover, induced supervisor, and normality of the reduced supervisor w.r.t. the original supervisor. In this paper, it is proved that the reduced supervisor, constructed by the proposed method in [9], preserves the observation properties, i.e. normality and relative observability, by self looping corresponding unobservable events at some states of the reduced supervisor. This property can be applied to find a natural projection, under which the supervisor is relative observable.

Vahid Saeidi, Ali A. Afzalian, Davood Gharavian

Supervisor localization procedure can be used to construct local controllers corresponding to each component agent in discrete-event systems. This procedure is based on state reduction of a monolithic supervisor with respect to each set of controllable events corresponding to each component agent. State reduction from the reduced supervisor to each local controller is an important criterion. In this paper, we deal with event reduction. It is proved that the number of events in each local controller is less than the event cardinality in the reduced supervisor, provided that each local controller has less number of states comparing to the reduced supervisor. It shows that each local controller needs less number of events to make consistent decisions. Having this property, we can evaluate the localizability of a supervisor by event reduction criteria instead of state reduction criteria. State reduction facilitates the implementation of local controllers on industrial systems. Whereas, event reduction reduces communication traffic between each pair of local controllers.