Think globally, act locally: decentralized supervisory control
TL;DR: In this article, a necessary and sufficient condition is given for the existence of a solution to the problem of finding decentralized supervisors that ensure that the behavior of the closed-loop system lies in a given range.
Abstract: Decentralized supervisory control is investigated by considering problem formulations that model systems whose specifications are given as global constraints, but whose solution is described by local controllers. A necessary and sufficient condition is given for the existence of a solution to the problem of finding decentralized supervisors that ensure that the behavior of the closed-loop system lies in a given range. Where the range of behavior can be described by regular languages, it can be effectively tested whether the decentralized control problem is solvable; in this case, a procedure is given to compute the associated supervisors. >
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TL;DR: Dosing recommendations for azathioprine, mercaptopurine (MP), and thioguanine based on TPMT genotype are provided and homozygous wild‐type individuals show lower activeThiopurine nucleolides and less myelosuppression.
Abstract: Thiopurine methyltransferase (TPMT) activity exhibits monogenic co-dominant inheritance, with ethnic differences in the frequency of occurrence of variant alleles. With conventional thiopurine doses, homozygous TPMT-deficient patients (~1 in 178 to 1 in 3,736 individuals with two nonfunctional TPMT alleles) experience severe myelosuppression, 30-60% of individuals who are heterozygotes (~3-14% of the population) show moderate toxicity, and homozygous wild-type individuals (~86-97% of the population) show lower active thioguanine nucleolides and less myelosuppression. We provide dosing recommendations (updates at http://www.pharmgkb.org) for azathioprine, mercaptopurine (MP), and thioguanine based on TPMT genotype.
567 citations
TL;DR: It is shown that under this architecture, a larger class of languages can be achieved than before since a relaxed version of the notion of co-observability appears in the necessary and sufficient conditions for the existence of supervisors.
Abstract: We consider a generalized form of the conventional decentralized control architecture for discrete-event systems where the control actions of a set of supervisors can be “fused” using both union and intersection of enabled events. Namely, the supervisors agree a priori on choosing “fusion by union” for certain controllable events and “fusion by intersection” for certain other controllable events. We show that under this architecture, a larger class of languages can be achieved than before since a relaxed version of the notion of co-observability appears in the necessary and sufficient conditions for the existence of supervisors. The computational complexity of verifying these new conditions is studied. A method of partitioning the controllable events between “fusion by union” and “fusion by intersection” is presented. The algebraic properties of co-observability in the context of this architecture are presented. We show that appropriate combinations of fusion rules with corresponding decoupled local decision rules guarantee the safety of the closed-loop behavior with respect to a given specification that is not co-observable. We characterize an “optimal” combination of fusion rules among those combinations guaranteeing the safety of the closed-loop behavior. In addition, a simple supervisor synthesis technique generating the infimal prefix-closed controllable and co-observable superlanguage is presented.
267 citations
TL;DR: A general version of Zhong's hierarchical consistency is established by first achieving control consistency — preservation of control structures through the aggregation mapping in a two-level hierarchy.
Abstract: An abstract hierarchical control theory is developed for discrete-event systems, based on the concepts of control structures and observers. Control structure is an abstract generalization of the family of controllable sublanguages in the Ramadge-Wonham framework. We establish a general version of Zhong's hierarchical consistency by first achieving control consistency — preservation of control structures through the aggregation mapping in a two-level hierarchy. For a refinement of hierarchical consistency with preservation of nonblocking, the concept of observer is introduced via congruences on nondeterministic transition structures.
266 citations
Cites methods from "Think globally, act locally: decent..."
...Big advancements have been made, with the introduction of modular control [51], online control [11], decentralized control [ 39 ] and, as we will explore in greater detail in this paper, hierarchical control [54, 2, 3, 46, 27]....
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28 Jun 2003
TL;DR: The method proposed in this paper to solve a control problem consists in transforming this problem into a problem of satisfiability of a µ-calculus formula so that the set of models of this formula is exactly theSet of controllers that solve the problem.
Abstract: The synthesis of controllers for discrete event systems, as introduced by Ramadge and Wonham, amounts to computing winning strategies in parity games We show that in this framework it is possible to extend the specifications of the supervised systems as well as the constraints on the controllers by expressing them in the modal µ-calculusIn order to express unobservability constraints, we propose an extension of the modal µ-calculus in which one can specify whether an edge of a graph is a loop This extended µ-calculus still has the interesting properties of the classical one In particular it is equivalent to automata with loop testing The problems such as emptiness testing and elimination of alternation are solvable for such automataThe method proposed in this paper to solve a control problem consists in transforming this problem into a problem of satisfiability of a µ-calculus formula so that the set of models of this formula is exactly the set of controllers that solve the problem This transformation relies on a simple construction of the quotient of automata with loop testing by a deterministic transition system This is enough to deal with centralized control problems The solution of decentralized control problems uses a more involved construction of the quotient of two automataThis work extends the framework of Ramadge and Wonham in two directions We consider infinite behaviours and arbitrary regular specifications, while the standard framework deals only with specifications on the set of finite paths of processes We also allow dynamic changes of the sets of observable and controllable events
240 citations
TL;DR: Under this new framework, a series of new decentralized architectures are defined and studied, and the properties of their corresponding notions of decentralized diagnosability are characterized and their relationship with existing work described.
Abstract: Decentralized diagnosis of discrete event systems has received a lot of attention to deal with distributed systems or with systems that may be too large to be diagnosed by one centralized site. This paper casts the problem of decentralized diagnosis in a new hierarchical framework. A key feature is the exploitation of different local decisions together with appropriate rules for their fusion. This includes local diagnosis decisions that can be interpreted as "conditional decisions." Under this new framework, a series of new decentralized architectures are defined and studied. The properties of their corresponding notions of decentralized diagnosability are characterized and their relationship with existing work described. Corresponding verification algorithms are also presented and on-line diagnosis strategies discussed.
160 citations
References
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Book•
01 Jan 1979
TL;DR: This book is a rigorous exposition of formal languages and models of computation, with an introduction to computational complexity, appropriate for upper-level computer science undergraduates who are comfortable with mathematical arguments.
Abstract: This book is a rigorous exposition of formal languages and models of computation, with an introduction to computational complexity. The authors present the theory in a concise and straightforward manner, with an eye out for the practical applications. Exercises at the end of each chapter, including some that have been solved, help readers confirm and enhance their understanding of the material. This book is appropriate for upper-level computer science undergraduates who are comfortable with mathematical arguments.
13,779 citations
TL;DR: In this paper, the control of a class of discrete event processes, i.e., processes that are discrete, asynchronous and possibly non-deterministic, is studied. And the existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language, where the control process is described as the generator of a formal language, while the supervisor is constructed from the grammar of a specified target language that incorporates the desired closed-loop system behavior.
Abstract: This paper studies the control of a class of discrete event processes, i.e. processes that are discrete, asynchronous and possibly nondeter-ministic. The controlled process is described as the generator of a formal language, while the controller, or supervisor, is constructed from the grammar of a specified target language that incorporates the desired closed-loop system behavior. The existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language. Two examples are provided.
3,432 citations
01 Apr 1988
TL;DR: The observability of discrete-event systems is investigated and a solution of the supervisory control and observation problem (SCOP) is obtained.
Abstract: The observability of discrete-event systems is investigated. A discrete-event system G is modeled as the controlled generator of a formal language L m ( G ) in the framework of Ramadge and Wonham. To control G, a supervisor S is developed whose action is to enable and disable the controllable events of G according to a record of occurrences of the observable events of G, in such a way that the resulting closed-loop system obeys some prespecified operating rules embodied in a given language K. A necessary and sufficient condition is found for the existence of a supervisor S such that L m ( S/G ) = K . Based on this condition, a solution of the supervisory control and observation problem (SCOP) is obtained. Two examples are provided.
834 citations
TL;DR: In this paper, the supremal controllable sublanguage S of a given language L is characterized as the largest fixpoint of a monotone operator, and the fixpoint S can be computed as the limit of the (finite) sequence given by the language.
Abstract: The concept of controllable language has been shown to play a basic role in the existence theory of supervisory controls for discrete event processes. In this paper the supremal controllable sublanguage S of a given language L is characterized as the largest fixpoint of a monotone operator $\Omega $. In the case where the languages involved are regular it is shown that the fixpoint S can be computed as the limit of the (finite) sequence $\{ {K_j } \}$ given by $K_{j + 1} = \Omega (K_j )$, $K_0 = L$. An effective computational algorithm is developed, and three examples are provided for illustration.
749 citations
TL;DR: Extends certain aspects of the work of P.J. Ramadge and W.M. Wonham on the control of a class of discrete-event processes to the case of decentralized control.
Abstract: Extends certain aspects of the work of P.J. Ramadge and W.M. Wonham (see SIAM J. Control Optimiz., vol.25, Jan. 1987) on the control of a class of discrete-event processes. The controlled process is described by a language L having strings that specify the sequences of events sigma /sub 1/ . . . sigma /sub n/ that the process can execute. The controller makes partial observations on the process events. Based on these observations the controller must enable or disable certain process events so that the resulting language generated by the closed-loop process is the specified sublanguage K contained in/implied by L. The case of decentralized control in which there are several controllers each of which makes partial observations and controls a subset of the process events is also studied. The results are illustrated for an example of communication protocols. >
587 citations