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.     

Formulas for calculating supremal controllable and normal sublanguages

Supremal controllable and normal sublanguages have been shown to play an important role in supervisor synthesis. In this paper, we discuss the computation of supremal controllable and normal sublanguages. We derive formulas for both supremal controllable sublanguages and supremal normal sublanguages when the languages involved are closed. As a result, those languages can be computed without applying recursive algorithms. We also discuss those aspects of these formulas.     

Synthesis of controllable and normal sublanguages for discrete-event systems using a coordinator

Synthesis of normal or controllable and normal sublanguages of global specification languages without computation of the global modular plant is a difficult problem. In this paper, these sublanguages are computed using a coordinator. We recall the notion of conditional controllability, introduce a notion of conditional normality, and prove necessary and sufficient conditions where such a computation is possible. Specifically, we show that conditionally controllable and conditionally normal languages computed by our method are controllable and normal with respect to the global plant. The optimality (supremality) of the resulting languages is also discussed.     

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.     

On supremal languages of classes of sublanguages that arise in supervisor synthesis problems with partial observation

This paper characterizes the class of closed and (M, N)-recognizable languages in terms of certain structural aspects of relevant automata. This characterization leads to algorithms that effectively compute the supremal (M, N)-recognizable sublanguage of a given language. One of these algorithms is used, in an alternating manner with an algorithm which yields the supremal (∑_u, N)-invariant resulting algorithm is proved. An example illustrates the use of these algorithms. This research was supported in part by the Air Force Office of Scientific Research under Grant No. AFOSR-86-0029, in part by the National Science Foundation under Grant No. ECS-8412100, and in part by the DoD Joint Services Electronics Program through the Air Force Office of Scientific Research (AFSC) Contract No. F49620-86-C-0045     

Maximally permissive mutually and globally nonblocking supervision with application to switching control

A supervisor is said to be mutually nonblocking with respect to a pair of specifications if upon completing a task in any of the specifications, it can continue on to complete the task in the other specification, i.e., the two specifications do not block each other. The notion of mutually nonblocking supervisor was introduced in Fabian and Kumar [2000. Automatica, 36(12), 1863-1869]. In this paper, we present an algorithm of polynomial complexity for computing a maximally permissive mutually and globally nonblocking supervisor. In case such a supervisor does not exist, we present a technique for relaxing the specifications for which a supervisor exists. The algorithms are based on a notion of attractability, and as a special case offer a new way of computing the maximally permissive nonblocking supervisors. The results are then applied to design of maximally permissive switching supervisors so as to allow for switching between the specifications at any time while the system is executing.     

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.     

On the control of discrete-event dynamical systems

We study a class of problems related to the supervisory control of a discrete-event system (DES), as formulated by Ramadge and Wonham, and we focus on the computational effort required for their solution. While the problem of supervisory control of a perfectly observed DES may be easily solved by dynamic programming, the problem becomes intractable (in the sense of complexity theory) when imperfectly observed systems are considered. Research supported by the Army Research Office (Grant No. DAAL03-86-K-0171) and by an NSF PYI award, with matching funds from Bellcore Inc.     

Supervisory control of switching control systems

In this paper, the problem of designing a switching policy for an adaptive switching control system is formulated as a problem of supervisory control of a discrete-event system (DES). Two important problems in switching control are then addressed using the DES formulation and the theory of supervisory control under partial observation. First, it is verified whether for a given set of controllers, a switching policy satisfying a given set of constraints on the transitions among controllers exists. If so, then a minimally restrictive switching policy is designed. Next, an iterative algorithm is introduced for finding a minimal set of controllers for which a switching policy satisfying the switching constraints exists. It is shown that in the supervisory control problem considered in this paper, limitations on event observation are the factors that essentially restrict supervisory control. In other words, once observation limitations are respected, limitations on control will be automatically satisfied. This result is used to simplify the proposed iterative algorithm for finding minimal controller sets.     

Compositional Synthesis of Maximally Permissive Supervisors Using Supervision Equivalence

This paper presents a general framework for efficient synthesis of supervisors for discrete event systems. The approach is based on compositional minimisation, using concepts of process equivalence. In this context, a large number of ways are suggested how a finite-state automaton can be simplified such that the results of supervisor synthesis are preserved. The proposed approach yields a compact representation of a least restrictive supervisor that ensures controllability and nonblocking. The method is demonstrated on a simple manufacturing example to significantly reduce the number of states constructed for supervisor synthesis.

Lose Fat, Not Muscle: An Examination of Supervisor Reduction in Discrete-Event Systems

This paper is concerned with the elimination of unnecessary states in discrete-event system control agents. Several approaches to supervisor reduction are studied and a new relation between agents, comparability, is defined to encapsulate most of the concepts found in the aforementioned methods. This relation is also proven to be preserved under conjunction, which is commonly employed to determine the centralized representation of two decentralized DES supervisors.

Modular supervisory control of discrete-event systems

A modular approach to the supervisory control of a class of discrete-event systems is formulated, and illustrated with an example. Discrete-event systems are modeled by automata together with a mechanism for enabling and disabling a subset of state transitions. The basic problem of interest is to ensure by appropriate supervision that the closed loop behavior of the system lies within a given legal behavior. Assuming this behavior can be decomposed into an intersection of component restrictions, we determine conditions under which it is possible to synthesize the appropriate control in a modular fashion. The work of this author was supported by NSERC (Canada) under Grant No. A-7399. The work of this author was supported by the National Science Foundation through Grant No. ECS-8504584.     

Synthesis of product-driven coordination controllers for a class of discrete-event manufacturing systems

A synthesis approach is proposed for discrete-event coordination architectures applied to a class of automated manufacturing systems (AMS) in which a clear separation is established between equipment control activities and product manufacturing procedures. Manufacturing procedures are modeled by regular languages constructed with a class of control commands named imperative. Equipment controllers are synthesized as a standard discrete-event supervisors dealing only with operational and safety issues of equipment groupings. The control of equipment modules is carried out following the imperative control commands sequences. Conditions are established to guarantee that the manufacturing procedure of a given product can be achieved using the synthesized supervisors in a particular AMS. Therefore, equipment controllers are not needed to be modified to consider the manufacturing of different products, whilst the construction of achievable manufacturing procedures becomes an “ad hoc” simple process using a reduced set of procedural blocks. The approach is illustrated with an experimental AMS.     

On perturbations of linear controllable infinite-dimensional time-varying discrete-time systems

It is shown that for a broad class of linear (possibly time-varying and infinite-dimensional) discrete-time systems x_k+1 = A_kx_k + B_ku_k the property of being uniformly equicontrollable is preserved under small perturbations of system parameters. The problem of controllability of asymptotically time-invariant systems is also studied.     

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.     

Online control of discrete-event systems: A survey

In control theory, as in other areas of engineering research, there is an inherent tension between the breadth of a technique’s applicability and its mathematical tractability. For the area of discrete-event systems (DES), this manifested itself in a theory of supervisory control that originally provided correct-by-construction guarantees for offline solutions to a restricted kind of deterministic process. Follow-on work extended the reach of these techniques to a number of new settings, notably the development of online control without sacrificing any of the original DES performance guarantees. The ability to enact online control opened the door to applying DES techniques to the adaptive control processes presented by modern technologies: processes with dynamic and time-varying natures, whose characteristics may be understood poorly or not at all. Although many works have built on the seminal work of online control in DES, we believe that these ideas have not reached their full potential due to the difficulty in translating them to adjacent fields. In this survey, we look back at 30 years of research concerning the online control of DES and closely related limited lookahead policies with an eye to making the works accessible to practitioners in the broader control theory and artificial intelligence communities. We conclude with some thoughts on future research directions for the further development and application of online DES control techniques to problems requiring intelligent control in our modern world.     

On controllability,near-controllability,controllable subspaces,and nearly-controllable subspaces of a class of discrete-time multi-input bilinear systems

This paper considers a class of discrete-time multi-input inhomogeneous bilinear systems. The structure of such systems is most close to linear time-invariant systems’ but they own a strong property. That is, if the systems are uncontrollable, they can still be nearly controllable. Necessary and sufficient conditions for controllability and near-controllability of the systems are established by using a classical decomposition. Furthermore, a geometric characterization is given for the systems such that controllable subspaces and nearly-controllable subspaces are derived and characterized. Similar results on controllability are also obtained for the continuous-time counterparts of the systems. Finally, examples are provided to demonstrate the conceptions and results of this paper.     

Designing communicating transaction processes by supervisory control theory

A Communicating Transaction Process (CTP) is a computational model that serves as a high level specification language for reactive embedded system components and their interactions. It consists of a network of communicating processes coordinating their behaviors via common actions and the common actions are refined as a set of guarded Message Sequence Charts (MSCs). There has been little work devoted to developing CTP models systematically. This paper takes the first step towards bridging this gap. In our work, communicating processes of embedded components are modeled and controlled as Discrete-Event Systems (DES). The control logic among communicating components is derived by Supervisory Control Theory (SCT), so as to guarantee that the communicating processes meet all predefined constraints and possess other desirable system behavioral properties. The control logic is then translated into propositional formulas for guarded MSCs which then results in a CTP model with guaranteed behavioral properties.     

The relationship of controllability between classical and fuzzy discrete-event systems

We have known that the controllability of classical discrete-event systems has already been extended into fuzzy discrete-event systems. In this paper, firstly, we recall some related definitions and results of the controllability for classical and fuzzy discrete-event systems, respectively. Secondly, we are concerned with the relationship of the controllability between classical and fuzzy discrete-event systems. In particular, we show that there is an equivalence of the controllability between the two systems to some extent, some special proofs are also presented. Finally, we use this equivalence to extend some general controllability properties of classical discrete-event systems into fuzzy ones.     

A learning-based synthesis approach todecentralized supervisory control of discrete event systems with unknown plants

In this paper, we consider the problem of automatic synthesis of decentralized supervisor for uncertain discrete event systems. In particular, we study the case when the uncontrolled plant is unknown a priori. To deal with the unknown plants, we first characterize the conormality of prefix-closed regular languages and propose formulas for computing the supremal conormal sublanguages; then sufficient conditions for the existence of decentralized supervisors are given in terms of language controllability and conormality and a learning-based algorithm to synthesize the supervisor automatically is proposed. Moreover, the paper also studies the on-line decentralized supervisory control of concurrent discrete event systems that are composed of multiple interacting unknown modules. We use the concept of modular controllability to characterize the necessary and sufficient conditions for the existence of the local supervisors, which consist of a set of local supervisor modules, one for each plant module and which determines its control actions based on the locally observed behaviors, and an on-line learning-based local synthesis algorithm is also presented. The correctness and convergence of the proposed algorithms are proved, and their implementation are illustrated through examples.