Son otuz yıl içerisinde bilgisayar, haberleşme ve elektronik teknolojisindeki hızlı gelişimin bir sonucu olarak yeni bir tür dinamik sistem ortaya çıkmıştır. Öyle ki bu tür dinamik sistemler incelendiğinde, büyük bir bölümünün çoğu zaman tamamının ayrık, zamandan bağımsız değişkenlerle kontrol edildiği görülmektedir. Üretim sistemleri, bilgisayar sistemleri, haberleşme sistemleri, hava trafik sistemleri gibi birçok sistem bu tür sistem sınıfına girmektedir. Bu tür sistemlerin davranışı genellikle eş zamansız olarak oluşan ayrık olaylara bağlı olarak değişir. Bu özellikleri nedeniyle bu sistemler Ayrık Olay Sistemleri olarak adlandırılmaktadır. Ayrık olay sistemi çok fazla olası kilitlenme içerdiğinde denetimsel gözetleyici olarak en az kısıtlamalı kilitlenmesiz çözümü seçmek tutucu bir çözüm oluşturabilir. O zaman toplam performansı arttırmak için kilitlenmesiz olma koşulunu esnetmek kaçınılmaz bir olgudur. Diğer bir taraftan tam başarımlı çözümü denetimsel gözetleyici olarak seçmek bazı olası kilitlenmelerden dolayı ciddi sistem arızalarına sebebiyet verebilir. O zaman bu iki sonucu bağlayan bir denetimsel gözetleyiciye ihtiyaç vardır. Bu yüzden bu çalışmada optimizasyon yaklaşımını kullanarak kilitlenme ve başarım arasındaki denge araştırılmıştır. İlk olarak kilitlenme ve başarılara karşılık gelen kelimelerin nümerik değerlerine dayanan yeni bir performans ederi ortaya çıkartılmıştır. Önerilen formülasyon klasik optimizasyon yaklaşımını barındıran temel değiş tokuş özelliğine sahiptir. Aynı zamanda istenilen işaretli dili olabildiğince üreten optimal kilitlenebilir çözümü araştıran yeni bir algoritma önerilmiştir.

We can not model discrete event systems by employing ordinary differential equations, this being their most important difference from time-varying dynamic systems. Rather discrete event systems evolve in time in the form of events occurring at possibly irregular time intervals. Therefore, we often model them as regular languages represented by deterministic finite state automata. In addition, in order to examine the behavior of the system, we modify the behavior by a control action. Ramadge and Wonham’s supervisory control theory is a powerful tool to build variety of modifications in the model through a supervisor. However, the supervisor can not usually mark all the desired behaviors of the system, which are built according to nonblocking and controllability constraints. Thus blocking becomes a crucial task in discrete event systems. Industrial examples give support to this observation too. We observe that supervisory control problems with blocking are generally more widespread than those without blocking, and blocking supervisors are preferred to nonblocking ones in several applications. Among these applications, database concurrency control, the protocols coupled with deadlock detection schemes are most popular since deadlock prevention and avoidance are impractical. When we examine a discrete event system within the corresponding admissible language, too many blockings may be realized. We then usually select minimally restrictive nonblocking solution as the supervisor, even though it is inadequate due to its restrictive behavior. Since it prevents all uncontrollable events that lead to blocking minimal restrictive nonblocking solution can provide a conservative result. As a result, the supervisor can generate only a small part of admissible marked language. As such this strategy may constrain the behavior of the system considerably. On the other hand, the completely satisfying solution generates all the admissible marked strings, but its price adds too many blockings to the supervised language. Therefore, neither of these two results can be acceptable in many discrete event system problems. Here the success of the supervisor is related to the generated admissible marked language. Then it will be of interest to relax the nonblocking requirement and consider the synthesis of blocking supervisors. What motivates us to consider blocking solutions is that by allowing a certain amount of blocking, we can increase the part of admissible marked language that can be achieved under control. At this point the following question needs to be answered. “How many blockings do arise?” This work aims to find a formal answer to this question. In the literature blocking supervisors were first studied by Chen and Lafortune. If possible, the proposed solution may improve the performance either by reducing the supervised language’s blocking without affecting its achievement or by increasing the supervised language’s achievement without affecting its blocking. But, the literature did not concern with improving the performance by reducing the blockings and achievements at the same time. Furthermore, the generated strings on the system have different meanings in practice. For example, some strings, which symbolize critic tasks, have high importance compared to other strings. Thus the differences between the strings have to be taken into consideration to select the best supervisor. In this work, we propose a new approach to overcome these drawbacks. Firstly, we suggest a new metric space and introduce a new performance measure including blocking. The performance of blocking supervisors hold on two concepts: blocking and failure. The defined performance measure captures the fundamental concept, as it is given over sum of blocking measure and non-satisfying measure. Afterwards we propose a new method to select an optimal blocking but also maximally permissive supervisor from the acceptable solution set. The proposed algorithm removes some strings in a sequence from the initial language in order to optimize the performance. As it is usually required to generate as many as possible admissible marked strings, the complete satisfying solution is selected as the initial language. Also it is proved that the final solution obtained will be the maximally permissive and the optimal blocking supervisor. Also, the method is explained over a database management system.