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     

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.     

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.     

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.     

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.     

Online supervisor synthesis for partially observed discrete-eventsystems

A partial information supervisor that generates a class of closed controllable and observable sublanguages of a specified “legal” language is presented. This supervisor has the following features: 1) it can be implemented online (i.e., the disabled event set need only be computed once upon each event observation); 2) the computations of the disabled event set can be performed in O(mn) worst case complexity, where a is the number of states in the legal language generator and m is the number of events; 3) an online supervisor presented previously by Heymann and Lin (1993) is a special case of the new supervisor; and 4) all the languages generated by the new supervisor contain the supremal closed controllable and normal (supCCN) sublanguage of the legal language (in fact, they contain a language developed by Fa et al. (1993) that was shown to contain the supCCN sublanguage)     

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 computation of supremal controllable, normal sublanguages

In this paper, we present an algorithm for the computation of the controllable, normal sublanguage of a given language, encountered in the solution of the supervisory control of discrete-event systems under partial observation. The algorithm produces the desired result under certain assumptions on the plant and the event projection map. In particular, the plant has to be nonblocking. The advantage of the algorithm over the solution available in the literature is that it does not involve iterations on the supremal controllable sublanguage and supremal normal sublanguage operators.     

Synthesis of Inference-Based Decentralized Control for Discrete Event Systems

In our past work, we presented a framework for the decentralized control of discrete event systems involving inferencing over ambiguities, about the system state, of various local decision makers. Using the knowledge of the self-ambiguity and those of the others, each local control decision is tagged with a certain ambiguity level (level zero being the minimum and representing no ambiguity). A global control decision is taken to be a "winning" local control decision, i.e., one with a minimum ambiguity level. For the existence of a decentralized supervisor, so that for each controllable event the ambiguity levels of all winning disablement or enablement decisions are bounded by some number N (such a supervisor is termed N-inferring), the notion of N- inference-observability was introduced. When the given specification fails to satisfy the iV-inference-observability property, an iV-inferring supervisor achieving the entire specification does not exist. We first show that the class of iV-inference-observable sublanguages is not closed under union implying that the supremal N- inference-observable sublanguage need not exist. We next provide a technique for synthesizing an N -inferring decentralized supervisor that achieves an N -inference-observable sublanguage of the specification. The sublanguage achieved equals the specification language when the specification itself is iV-inference-observable. A formula for the synthesized sublanguage is also presented. For the special cases of N = 0 and N = 1, the proposed supervisor achieves the same language as those reported in [25], [31] (for N = 0) and [32] (for N = 1). The synthesized supervisor is parameterized by N (the parameter bounding the ambiguity level), and as N is increased, the supervisor becomes strictly more permissive in general. Thus, a user can choose N based on the degree of permissiveness and the degree of computational complexity desired.     

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.     

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.     

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     

Observability and decentralized control of fuzzy discrete-event systems

Fuzzy discrete-event systems as a generalization of (crisp) discrete-event systems have been introduced in order that it is possible to effectively represent uncertainty, imprecision, and vagueness arising from the dynamic of systems. A fuzzy discrete-event system has been modeled by a fuzzy automaton; its behavior is described in terms of the fuzzy language generated by the automaton. In this paper, we are concerned with the supervisory control problem for fuzzy discrete-event systems with partial observation. Observability, normality, and co-observability of crisp languages are extended to fuzzy languages. It is shown that the observability, together with controllability, of the desired fuzzy language is a necessary and sufficient condition for the existence of a partially observable fuzzy supervisor. When a decentralized solution is desired, it is proved that there exist local fuzzy supervisors if and only if the fuzzy language to be synthesized is controllable and co-observable. Moreover, the infimal controllable and observable fuzzy superlanguage, and the supremal controllable and normal fuzzy sublanguage are also discussed. Simple examples are provided to illustrate the theoretical development.     

Blocking and controllability of Petri nets in supervisory control

This note discusses the use of Petri net languages in supervisory control theory. First it is shown that the trimming of an unbounded Petri net is not always possible and a new class of Petri net languages, that may be generated by nonblocking nets, is defined. Secondly, necessary and sufficient conditions for the existence of a Petri net supervisor, under the hypothesis that the system's behavior and the legal behavior are both Petri net languages, are derived. Finally, by means of an example, it is shown that Petri net languages are not closed under the supremal controllable sublanguage operator     

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.     

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.     

Controllability of predicates and languages in discrete-event systems

In discrete-event systems, two control techniques, called supervisory control and state feedback logic, are applicable if control specifications are given in terms of predicates on the set of states. The concepts of controllability for both techniques has been proposed for the analysis and design of these techniques. First it is shown that controllability of the legal language for a given predicate is equivalent to that for the corresponding reachability set. Next we deal with the relationship between the supremal controllable subpredicate of the predicate and the supremal controllable sublanguage of the corresponding legal language     

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.     

Supervisory control of fuzzy discrete event systems.

To cope with situations in which a plant's dynamics are not precisely known, we consider the problem of supervisory control for a class of discrete event systems modeled by fuzzy automata. The behavior of such discrete event systems is described by fuzzy languages; the supervisors are event feedback and can only disable controllable events with any degree. In this new sense, we present a necessary and sufficient condition for a fuzzy language to be controllable. We also study the supremal controllable fuzzy sublanguage and the infimal controllable fuzzy superlanguage.     

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。