An algorithm for computing the mask value of the supremal normalsublanguage of a legal language

We consider the problem of finding the mask value of the supremal normal sublanguage L_R of some given language L. We describe a straightforward algorithmic solution that can be applied to existing off-line procedures for determining the supremal controllable and normal sublanguage of L and that does not require an explicit calculation of L _R. This problem is fundamental because it is related to the supervisory control problem under partial observation. Our algorithm applies only to closed languages     

On supervisory control of sequential behaviors

The authors address the supervisory synthesis problem of controlling the sequential behaviors of discrete-event dynamical systems (DEDSs) under complete and partial information through the use of synchronous composition of the plants and the supervisors. The authors present the notion of complete languages, discuss some of its algebraic properties, and show its close relation to ω-languages. The authors prove that the supremal (closed) complete and controllable sublanguage of a given language exists, and present an algorithm to compute it. They present a closed-form expression for the supremal ω-controllable sublanguage of a given ω-language in terms of the supremal (closed) complete and controllable sublanguage. This closed-form expression suggests that certain operations on a given ω-language can alternatively be achieved by performing certain other similar operations on its prefix (which is a finite language) and then taking the limit (to obtain the desired ω-language). A necessary and sufficient condition for the existence of a supervisor in case of partial observation is presented in terms of ω-observability. Notion of ω-normality is also introduced, and a closed-form expression for the supremal ω-normal sublanguage, in terms of the supremal closed, complete, and normal sublanguage, is presented     

On-line control of partially observed discrete event systems

It is well known that the design of supervisors for partially observed discrete-event systems is an NP-complete problem and hence computationally impractical. Furthermore, optimal supervisors for partially observed systems do not generally exist. Hence, the best supervisors that can be designed directly for operation under partial observation are the ones that generate the supremal normal (and controllable) sublanguage. In the present paper we show that a standard procedure exists by which any supervisor that has been designed for operation under full observation, can be modified to operate under partial observation. When the procedure is used to modify the optimal full-observation supervisor (i.e., the one that generates the supremal controllable language), the resultant modified supervisor is at least as efficient as the best one that can be designed directly (that generates the supremal normal sublanguage). The supervisor modification algorithm can be carried out on-line with linear computational complexity and hence makes the control under partial observation a computationally feasible procedure.     

Distributed computation of supremal conditionally controllable sublanguages

In this paper, we further develop the coordination control framework for discrete-event systems with both complete and partial observations. First, a weaker sufficient condition for the computation of the supremal conditionally controllable sublanguage and conditionally normal sublanguage is presented. Then we show that this condition can be imposed by synthesising a-posteriori supervisors. The paper further generalises the previous study by considering general, non-prefix-closed languages. Moreover, we prove that for prefix-closed languages the supremal conditionally controllable sublanguage and conditionally normal sublanguage can always be computed in the distributed way without any restrictive conditions we have used in the past.     

A New Class of Supervisors for Timed Discrete Event Systems Under Partial Observation

Brandin and Wonham have developed a supervisory control framework for timed discrete event systems (TDESs) in order to deal with not only logical specifications but also temporal specifications. Lin and Wonham have extended this framework to the partial observation case, and presented necessary and sufficient conditions for the existence of a nonblocking supervisor under partial observation. In this paper, we define a new class of supervisors for TDESs under partial observation. We then present necessary and sufficient conditions for the existence of a nonblocking supervisor defined in this paper. These existence conditions of our supervisor are weaker than those of Lin and Wonham's supervisor. Note, however, that the price that must be paid to weaken the existence conditions is the higher computational cost. Moreover, given a closed regular language, we study computation of a sublanguage that satisfies the existence conditions of our supervisor. We present an algorithm for computing such a sublanguage larger than the supremal closed, controllable, and normal sublanguage.     

Robust nonblocking supervisory control of discrete-event systems

In this note, we generalize a robust supervisory control framework to deal with marked languages. We show how to synthesize a supervisor to control a family of plant models, each with its own specification. The solution we obtain is the most general in that it provides the closest approximation to the supremal controllable sublanguage for each plant/specification pair. We end the note by extending these results to deal with timed discrete-event systems.     

A Note on the Properties of the Supremal Controllable Sublanguage in Pushdown Systems

Consider an event alphabet Sigma. The supervisory control theory of Ramadge and Wonham asks the question: given a plant model G with language L_M (G) sube Sigma* and another language K sube L_M (G), is there a supervisor phi such that L_M (phi/G) = K? Ramadge and Wonham showed that a necessary condition for this to be true is the so-called controllability of K with respect to L_M (G). They showed that when G is a finite-state automaton and K is a regular language (also generated by a finite state automaton), then there is a regular supremal controllable sublanguage sup_C (K) sube K that is effectively constructable from generators of K and G. In this paper, we show: 1) there is an algorithm to compute the supremal controllable sublanguage of a prefix closed K accepted by a deterministic pushdown automaton (DPDA) when the plant language is also prefix closed and accepted by a finite state automaton and 2) in this case, we show that this supremal controllable sublanguage is also accepted by a DPDA.     

Supervisor Reduction for Discrete-Event Systems

In supervisory control theory (SCT) the supremal supervisor (representing the supremal controllable sublanguage) typically has a large state size (of order the product of state sizes of the plant and specification automata). In this paper, we propose an algorithm which can significantly reduce supervisor size while preserving control action. We also show that finding a supervisor of minimal size is NP-hard.     

Relative coobservability for decentralised supervisory control of discrete-event systems

In this paper, we study the concept of relative coobservability in decentralised supervisory control of discrete-event systems under partial observation. This extends our previous work on relative observability from a centralised setup to a decentralised one. A fundamental concept in decentralised supervisory control is coobservability (and its several variations); this property is not, however, closed under set union, and hence there generally does not exist the supremal element. Our proposed relative coobservability, although stronger than coobservability, is algebraically well behaved, and the supremal relatively coobservable sublanguage of a given language exists. We present a language-based algorithm to compute this supremal sublanguage; the algorithm allows straightforward implementation using off-the-shelf algorithms. Moreover, relative coobservability is weaker than conormality, which is also closed under set union; unlike conormality, relative coobservability imposes no constraint on disabling unobservable controllable events.     

一类上限能控子语言的N步递推求算解法

本文给出了基于Ｌ（Ｇ）的Ｎ步投影状态，递推求妥妥前缀闭合语言Ｋ的上限能控子语言算法。讨论了算法的单调性和最优性。     

Centralized and distributed algorithms for on-line synthesis of maximal control policies under partial observation

This paper deals with the on-line control of partially observed discrete event systems (DES). The goal is to restrict the behavior of the system within a prefix-closed legal language while accounting for the presence ofuncontrollable andunobservable events. In the spirit of recent work on the on-line control of partially observed DES (Heymann and Lin 1994) and on variable lookahead control of fully observed DES (Ben Hadj-Alouane et al. 1994c), we propose an approach where, following each observable event, a control action is computed on-line using an algorithm oflinear worst-case complexity. This algorithm, calledVLP-PO, has the following additional properties: (i) the resulting behavior is guaranteed to be amaximal controllable and observable sublanguage of the legal language; (ii) different maximals may be generated by varying the priorities assigned to the controllable events, a parameter ofVLP-PO; (iii) a maximal containing the supremal controllable and normal sublanguage of the legal language can be generated by a proper selection of controllable event priorities; and (iv) no off-line calculations are necessary. We also present a parallel/distributed version of theVLP-PO algorithm calledDI-VLP-PO. This version uses several communicating agents that simultaneously run (on-line) identical versions of the algorithm but on possibly different parts of the system model and the legal language, according to the structural properties of the system and the specifications. While achieving the same behavior asVLO-PO, DI-VLP-PO runs at a total complexity (for computation and communication) that is significantly lower than its sequential counterpart.     

Characterizations and effective computation of supremal relatively observable sublanguages

Recently we proposed relative observability for supervisory control of discrete-event systems under partial observation. Relative observability is closed under set unions and hence there exists the supremal relatively observable sublanguage of a given language. In this paper we present a new characterization of relative observability, based on which an operator on languages is proposed whose largest fixpoint is the supremal relatively observable sublanguage. Iteratively applying this operator yields a monotone sequence of languages; exploiting the linguistic concept of support based on Nerode equivalence, we prove for regular languages that the sequence converges finitely to the supremal relatively observable sublanguage, and the operator is effectively computable. Moreover, for the purpose of control, we propose a second operator that in the regular case computes the supremal relatively observable and controllable sublanguage.     

Supervisory control of deterministic Petri nets with regularspecification languages

Algorithms for computing a minimally restrictive control in the context of supervisory control of discrete-event systems have been well developed when both the plant and the desired behaviour are given as regular languages. In this paper the authors extend such prior results by presenting an algorithm for computing a minimally restrictive control when the plant behaviour is a deterministic Petri net language and the desired behaviour is a regular language. As part of the development of the algorithm, the authors establish the following results that are of independent interest: i) the problem of determining whether a given deterministic Petri net language is controllable with respect to another deterministic Petri net language is reducible to a reachability problem of Petri nets and ii) the problem of synthesizing the minimally restrictive supervisor so that the controlled system generates the supremal controllable sublanguage is reducible to a forbidden marking problem. In particular, the authors can directly identify the set of forbidden markings without having to construct any reachability tree     

Supervisory control using augmented languages in discrete event systems

This paper introduces the concept of an augmented (super) language of a specified language and studies its application to finite state supervisory control. First, we investigate several properties of an augmented language, especially related to controllability of the specified language. We propose an algorithm for the computation of a controllable sublanguage for which a finite state supervisor exists, using an augmented language, and show a sufficient condition for the controllable sublanguage to be supremal. It is shown, however, that such a finite state supervisor is sometimes blocking. Moreover, we discuss the relationship between the Wonham-Ramadge algorithm and our proposed one.     

On the language generated under fully decentralized supervision

This paper studies the language generated under fully decentralized supervision proposed by Kozak and Wonham (1995). The author assumes that desirable behavior is specified as a closed language. A closed-form expression for the language generated under fully decentralized supervision is presented. It is shown that the generated language is larger than the supremal closed, controllable, and strongly decomposable sublanguage. Moreover, a necessary and sufficient condition is derived for the generated language to be the supremal closed and controllable sublanguage     

On the supremal controllable sublanguage in the discrete-eventmodel of nondeterministic hybrid control systems

This paper is concerned with the logical control of hybrid control systems (HCS). It is assumed that a discrete-event system (DES) plant model has already been extracted from the continuous-time plant. The problem of hybrid control system design can then be solved by applying logical DES controller synthesis techniques to the extracted DES plant. Traditional DES synthesis methods, however, are not always applicable since the extracted plant DES will often exhibit nondeterministic transitions. This paper presents an extension of certain DES controller synthesis techniques to the nondeterministic control automaton found in HCS. In particular, this paper derives a formula computing the supremal controllable sublanguage of a given specification language under the assumption that the DES plant exhibits nondeterministic transitions     

Solvability of Centralized Supervisory Control Under Partial Observation

The problem of synthesizing a nontrivial controllable and observable sublanguage of a given non-prefix-closed language is addressed. This problem arises in supervisory control of discrete-event systems, when the objective is to synthesize safe nonblocking supervisors for partially observed systems. The decentralized version of this problem is known to be unsolvable. We show that the centralized version of this problem is solvable by presenting a new algorithm that synthesizes a nontrivial controllable and observable sublanguage of the given non-prefix-closed language, if one exists. We also show that the union of all nonblocking solutions to the associated supervisory control problem can be expressed as the union of all regular nonblocking solutions. This work was done when the first author was at the University of Michigan as a Ph.D. student.     

A modified normality condition for decentralized supervisory control of discrete event systems

In this paper, we study nonblocking decentralized supervisory control of discrete event systems. We introduce a modified normality condition defined in terms of a modified natural projection map. The modified normality condition is weaker than the original one and stronger than the co-observability condition. Moreover, it is preserved under union. Given a marked language specification, there exists a nonblocking decentralized supervisor for the supremal sublanguage which satisfies L_m(G)-closure, controllability, and modified normality. Such a decentralized supervisor is more permissive than the one which achieves the supremal L_m(G)-closed, controllable, and normal sublanguage.     

Formulas for a class of controllable and observable sublanguages larger than the supremal controllable and normal sublanguage

In this paper, we give some new methods for synthesis of controllers of discrete event dynamical systems (DEDS) with partial event informations. Given a regular target language L, we construct some effective computable algorithms for computing the controllable and observable sublanguages of L. We show that any one of these controllable and observable sublanguages obtained by our algorithms is larger than the supremal controllable and normal sublanguage of L.     

Decidability and closure properties of weak Petri net languages insupervisory control

We extend the class of control problems that can be modeled by Petri nets considering the notion of weak terminal behavior. Deterministic weak languages represent closed-loop terminal behaviors that may be enforced by nonblocking Petri net supervisors if controllable. The class of deterministic weak PN languages is not closed under the supremal controllable sublanguage operator