W. M. Wonham and P.J. Ramadge. Modular supervisory control of discrete event systems. Mathematics of Control, Signal and Systems, 1(1):13--30, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....on decentralized supervisory control were based upon a conjunctive fusion rule in which an event is enabled if and only if all local supervisors enable it. The usage of such a fusion rule by default may have been in uenced by the conjunctive architecture of modular control. In modular control [27], a speci cation is given as a conjunction of several sub speci cations, and a conjunction of sub supervisors enforcing the individual subspeci cations is used to achieve the overall speci cation. It is now understood that neither the modular control nor the decentralized control have to have a ....

W. M. Wonham and P. J. Ramadge, \Modular supervisory control of discrete-event systems, " Math. Contr. Signals Syst., vol. 1, no. 1, pp. 13-30, 1988.

....with the number of its components. This restricting factor, that is specially relevant for large scale systems, has been considered by several authors that attempt to overcome these computational difficulties by exploiting different aspects of the system, as symmetry ( EC98] or modularity ([WR88]) CAPES supported the first author and the second author was supported in part by CNPq. Most of large scale systems are modeled through the composition of many smaller subsystems usually representing concurrent operations. Their design is also characterized by having several specifications over ....

....composition of many smaller subsystems usually representing concurrent operations. Their design is also characterized by having several specifications over just a part of the global plant, in many cases intending to synchronize concurrent subsystems. For that reason, modular control, introduced in [WR88], is a natural solution to deal with such systems. It divides the overall task into subtasks and assigns them to different modular controllers. Instead of carrying out the design on a single, often large plant, the natural decentralized structure of large scale DES can also be exploited by ....

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W. M. Wonham and P. J. Ramadge. Modular supervisory control of discrete event systems. Mathematics of control of discrete event systems, 1(1):13-30, 1988.

....specification, is an obstacle in applications because the number of states that represent the system increases exponentially with the number of component elements of the system. This restricting factor has been considered by several authors that attempt to overcome these computational difficulties [WR88] [EC98a] EC98b] Bry86] This paper is about the modular control of composed systems, defined by local specifications. Local specifications are requirements referring to a specific part of the system to control, i.e. described on a subset of the events that affect the plant, as it is for ....

....systems, defined by local specifications. Local specifications are requirements referring to a specific part of the system to control, i.e. described on a subset of the events that affect the plant, as it is for example very often the case for manufacturing systems. The modularity property [WR88] assures the solution of the control problem through the synthesis of separate supervisors for each specification, without harming the global operation of the plant. However, the process of modularity verification found in the literature doesn t consider the properties of composed systems and it ....

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W. M. Wonham and P. J. Ramadge. Modular supervisory control of discrete event systems. Mathematics of control of discrete event systems, 1(1):13-30, 1988.

....property of the controlled system. These can be intersected to yield a global specification language. This procedure is subject to state space explosion just as in the case of a modular plant. Fortunately, in the case of modular specification, the principles of modular synthesis outlined in [23, 18] can be applied. The supervisory control problem is solved for each modular specification and the resulting supervisors are composed to form a solution to the globally specified problem. In addition to being more easily synthesized, a modular supervisor is easier to modify, update and maintain. ....

....(K 2 ; K 2 ) where K i = sup C(L spec i M P ) for i = 1; 2. Then, if K 1 and K 2 are non conflicting, a global least restrictive supervisor for the specification L spec = L spec 1 L spec 2 can be obtained by taking the composition of the modular supervisors S 1 and S 2 . It was shown in [23] that the total complexity of modular synthesis with n modules is O(n Theta jP j 2 (max i jL spec i j) 2 ) as opposed to O(jP j 2 (max i jL spec i j) 2n ) for the non modular synthesis. Note that the success of the non modular synthesis does not imply the success of the modular ....

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W.M. Wonham and P.J. Ramadge. Modular supervisory control of discrete event systems. Mathematics of Control Signals and Systems, 1:13--30, 1988.

....given as a set of specifications, each expressing only a few relevant aspects of the allowed and desired behavior of the closed loop system. The task of the supervisor is to make sure that all of the specifications are fulfilled as well as possible, simultaneously. Modular supervisory control (Wonham (1988)) has come to denote the type of control where two (or more) specifications are given, and the control objective is to keep the plant within as large a subset of the intersection of the specifications as possible. The intersection is a logical choice, since this guarantees that none of the ....

....The intersection is a logical choice, since this guarantees that none of the specifications are violated; only what they all agree upon is allowed. In some cases, supervisors can be calculated for each specification separately, with the conjunction of the supervisors controlling the system, see Wonham (1988). This automatically makes the closedloop system stay within the intersection of the specifications. Such a modular synthesis approach has many benefits in the regular case overcoming the combinatorial state space explosion problem, but it may also be too restrictive. In that case, the disjunction ....

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Wonham (1988). Wonham, W. M. and P. J. Ramadge, Modular Supervisory Control of Discrete Event Systems, Mathematics of Control, Signals and Systems, 1:13-30, 1988.

....commutes with the intersection operator. This means that a supremal supervisor generating (K 1 K 2 ) can be achieved in polynomial time, by applying the operator to each speci cation language and intersecting the results (K 1 K 2 ) We summarize the above results, taken from [16, 23]: 1. If K 1 and K 2 are non con icting, LM (G) closed and controllable, then K 1 K 2 is LM (G) closed and 10 s p a s s s s p p p p c a a c c a a a c p c a c a c a c a p p d d d d p d d d d d c d d d d d d c c c c s c p c c c c c c c c c c c c c c c 12 13 14 15 22 23 24 25 32 33 34 35 44 52 53 ....

W. Wonham and P. Ramadge. \Modular supervisory control of discrete event systems". Mathematical Control, Signals, and Systems 1(1):13-30, January 1988.

....Theory We present (from [RW90] and [RW92b] a problem formulation that describes a class of discreteevent systems subject to decentralized control. For more details on the formalities of supervisory control theory, the reader is referred to [RW82] Ram83] RW87] WR87] LW88] Won88] [WR88], LW90] Consider a discrete event process that can be characterized by an automaton G = Q; Sigma; ffi; q 0 ; Qm ) where Sigma is a finite alphabet of event labels (and represents the set of all possible events that can occur within the system) Q is a set of states, q 0 2 Q is the initial ....

....or (oe; y) disable enable otherwise: That is, T 1 Theta T 2 recognizes the intersection of the languages recognized by T 1 and T 2 and OE disables an event if and only if either OE or disables it. Thus, S 1 S 2 models the actions of S 1 and S 2 operating in parallel. It can be shown [WR88] that L(S 1 S 2 =G) L(S 1 =G) L(S 2 =G) and Lm (S 1 S 2 =G) Lm (S 1 =G) Lm (S 2 =G) Given a local supervisor S that controls some subset Sigma loc;c of Sigma c while observing some subset Sigma loc;o of Sigma, S denotes the supervisor which takes the same control action as S on ....

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W. M. Wonham and P. J. Ramadge. Modular supervisory control of discrete-event systems. Mathematics of Control, Signals, and Systems, 1:13--30, 1988.

....We have demonstrated the applicability of our work to computation of supervisors in control of logical behaviors of DESs, represented as languages over a certain event set, under complete as well as partial observation. The results presented here can also be applied for computation of modular [34] and decentralized [19, 29] supervisors, and also for computing supervisors for controlling the non terminating behaviors [25, 14, 32] The work presented here thus presents a unifying approach for existence and computation of supervisory control policies in a variety of settings. A Remark on ....

W. M. Wonham and P. J. Ramadge. Modular supervisory control of discrete event systems. Mathematics of Control Signals and Systems, 1(1):13--30, 1988.

....to be simpler than the global system. In that case, a polynomial time algorithm for computing the projected model is provided. As an application of our result on natural projections, we analyze the computational complexity involved in a decentralized control architecture along the lines of [WR88]. Having established that the observer property of the natural projection on a given system implies that the projected model is always simpler and its computation is at worst polynomial, the next natural question then is: how to arrange the observer property and at what cost This is a topic of ....

....behavior of that system) for which the projection will always simplify their generators and the computation of their projections is at worst polynomial. 4 An application As an application of the results in Section 3, we analyze a decentralized control architecture [LW88a, WW] along the lines of [WR88]. A notion of decentralized control of DES was formulated and studied in [LW88a] There local models of a global system are constructed by using natural projections on the behaviors of a global system. Specifications are given on the local models, and conditions are obtained to guarantee that ....

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W. M. Wonham and P. J. Ramadge. Modular supervisory control of discrete event systems. Mathematics of Control, Signal and Systems, 1(1):13--30, 1988.

....a simple command from outside. In this paper, we develop such a mechanism using finite state automata associated with each agent. These automata independently guide the agents, while taking into account feedback that captures the composite effect of all the agents actions. Ramadge and Wonham [5][9] give a similar treatment by means of discrete event decision systems (DEDS) but the conditions differ, as will be detailed below. We introduce this scheme with a simple game, called the Gur Game by Tsetlin [6] Imagine that we have N players, none of whom are aware of the others, and a referee. ....

....choosing A 1 goes to 1 as n 1. In other words, as the memory size gets larger, the automaton chooses the best option with increasing certainty. Here, there is only a single automaton, acting in isolation. This is basically the scenario developed by Ramadge and Wonham in their articles on DEDS [5][9]. However, while they do account for the possibility of nondeterminacy in the feedback mechanism, there is no explicit mention of a reward function, nor is there an attempt to optimize behavior in that context. Furthermore, even though it is possible to use the supervisory automata in these ....

W. Wonham and P. J. Ramadge. Modular supervisory control of discrete-event systems. Mathematics of Control, Signals, and Systems, Vol. 1(No. 1):13--30, 1988.

....of DEDS s. The computational complexity of the algorithm presented in [12] for constructing the minimally restrictive supervisor is quadratic [11] in the product of the number of states involved in the FSM realizations of the plant and that of the supervisor. It was mentioned without proof in [17] that if the languages describing the plant as well as the desired behavior are prefix closed, then the computational complexity of constructing the minimally restrictive supervisor is linear; however, no algorithm for the supervisor construction was given. We present an algorithm (Algorithm 3.10 ....

....have neglected the dependence of the computational complexity on any parameter other than m and n. Algorithm 3. 10 for constructing the generator for K is an order of magnitude faster than that in [12] The computational complexity of the algorithm in [12] is of order O(m 2 n 2 ) 11] In [17], it has been mentioned without proof that if the languages L(P ) and K are both assumed to be closed, then the computational complexity of constructing minimally restrictive supervisor is of order O(mn) however, no algorithm for the construction of the minimally restrictive supervisor is given. ....

W. M. Wonham and P. J. Ramadge. Modular supervisory control of discrete event systems. Mathematics of Control Signals and Systems, 1(1):13--30, 1988.

....or the occurrence of a binary input pattern in a digital logic circuit. Discrete event system models have been employed in the control and scheduling of manufacturing systems [2] in logical models such as queues and communication protocols [3,4,5] and in the study of decentralized control theory [4,6,7,8]. Discrete event models are generally used to describe systems where coordination and control is required to ensure the orderly flow of events, or to avoid the occurrence of certain chains of events. Like continuous time systems, a discrete event system can be in any one of a set of internal ....

Wonham, W. M. and Ramadge, P. J. "Modular Supervisory Control of Discrete Event Systems," Mathematics of Control, Signals and Systems, Jan. 1988, pp. 13--30.

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P. J. Ramadge and W. M. Wonham, 1988. Modular supervisory control of discrete event systems. Mathematics of Control, Signal and Systems, 1(1), pp. 13-30.

....an appraisal of the computational effort involved. 1 Introduction In the approach to supervisory control of discrete event systems (DES) based on controllable languages (for a survey see [RW89] 1 , different approaches to horizontal modularity (decentralized control) have been studied ( RW87] [WR88], CDFV88] LW88] RW92] and [WH91] These approaches can be roughly classified on the basis of whether the specification or the plant itself are modularized initially. In [WR88] the full specification language is expressed as the intersection of partial or specialized components, for which ....

....see [RW89] 1 , different approaches to horizontal modularity (decentralized control) have been studied ( RW87] WR88] CDFV88] LW88] RW92] and [WH91] These approaches can be roughly classified on the basis of whether the specification or the plant itself are modularized initially. In [WR88] the full specification language is expressed as the intersection of partial or specialized components, for which component supervisors are designed individually. The latter are envisaged to operate on line independently and concurrently. While the component supervisors are designed to be ....

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W. M. Wonham and P. J. Ramadge. Modular supervisory control of discrete event systems. Mathematics of Control, Signal and Systems, 1(1):13--30, 1988.

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W. M. Wonham and P.J. Ramadge. Modular supervisory control of discrete event systems. Mathematics of Control, Signal and Systems, 1(1):13--30, 1988.

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W.M. Wonham and P.J. Ramadge. Modular supervisory control of discrete event systems. Mathematics of Control, Signals and Systems, 1(1):13--30, 1988.

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W. M. Wonham and P. J. Ramadge. Modular supervisory control of discrete event systems. Mathematics of Control Signals and Systems, 1:13--30, 1988.

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W. M. Wonham and P. J. Ramadge. Modular supervisory control of discrete event systems. Mathematics of Control Signals and Systems, 1:13--30, 1988.

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W. M. Wonham and P. J. Ramadge. Modular supervisory control of discrete event systems. Mathematics of Control Signals and Systems, 1:13--30, 1988.

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W. M. Wonham and P. J. Ramadge. Modular supervisory control of discrete event systems. Mathematics of Control Signals and Systems, 1:13--30, 1988.

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