Hierarchical supervisory control of discrete event systems based on reliable events

Extends the formalism of prioritized synchronous composition (PSC), proposed by Heymann for modeling interaction (and control) of discrete event systems, to permit system interaction with their environment via interface masks. This leads to the notion of prioritized synchronous composition (MPSC), which we formally define, MPSC can be used to model interaction of systems at single as well as multiple interfaces. We show that MPSC can alternatively be computed by unmasking the PSC of masked systems, thereby establishing a link between MPSC and PSC. We next prove that MPSC is associative and thus suitable for modeling and analysis of supervisory control of discrete event systems. Finally, we use MPSC of a discrete event plant and a supervisor for controlling the plant behavior and show (constructively) that under the absence of driven events, controllability together with normality of the given specification serve as conditions for the existence of a supervisor. This extends the results on supervisory control, which permits control and observation masks to be associated with the plant only.

This paper extends the formalism of prioritized synchronous composition (PSC), proposed by Heymann (1990) for modeling interaction (and control) of discrete event systems, to permit system interaction with their environment via interface masks. This leads to the notion of prioritized synchronous composition (MPSC), which we formally define. We show that MPSC can alternatively be computed by unmasking the PSC of masked systems, thereby establishing a link between MPSC and PSC. We next show that MPSC is associative and thus suitable for modeling and analysis of supervisory control of discrete event systems. Finally, we use MPSC of a discrete event plant and a supervisor for controlling the plant behavior and show (constructively) that controllability together with normality of the given specification serve as conditions for the existence of a supervisor.

Networked control has been used more and more widely in engineering systems. To study networked control for discrete event systems, network controllability and network observability are introduced in our previous work on networked supervisory control theory. In this paper, we investigate robust supervisory control for networked discrete event systems. We assume that the system to be controlled is not known precisely. We only know that it is one among several possibilities. The goal is to design a robust supervisor that works for all possibilities. We derive a necessary and sufficient condition for the existence of such a robust supervisor. The condition must take into account the communication delays and losses in both observation channel and control channel. We show that the existence condition is characterized by network controllability and network observability that are keys to control networked discrete event systems.

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.

A hierarchical consistency problem for the hierarchical supervisory control of discrete event systems under partial observation is considered, since observability is a practical and general property in real systems. The notion of H-observability is introduced to ensure hierarchical consistency between low- and high-level systems, and an analytical framework for the hierarchical supervisory control is established.

Most prior work on supervisory control of discrete event systems is for achieving deterministic specifications, expressed as formal languages. In this paper we study supervisory control for achieving nondeterministic specifications. Such specifications are useful when designing a system at a higher level of abstraction so that lower level details of system and its specification are omitted to obtain higher level models that may be nondeterministic. Nondeterministic specifications are also meaningful when the system to be controlled has a nondeterministic model due to the lack of information (caused for example by partial observation or unmodeled dynamics). Language equivalence is not an adequate notion of behavioral equivalence for nondeterministic systems, and instead we use the finest known notion of equivalence, namely the bisimulation equivalence. Choice of bisimulation equivalence is also supported by the fact that bisimulation equivalence specification is equivalent to a specification in the temporal logic of /spl mu/-calculus that subsumes the complete branching-time logic CTL*. Given nondeterministic models of system and its specification, we study the design of a supervisor (possibly nondeterministic) such that the controlled system is bisimilar to the specification. We obtain a small model theorem showing that a supervisor exists if and only if it exists over a certain finite state space, namely the power set of Cartesian product of system and specification state spaces. Also, the notion of state-controllability is introduced as part of a necessary and sufficient condition for the existence of a supervisor. In the special case of deterministic systems, we provide an existence condition that can be verified polynomially in both system and specification states, when the existence condition holds.

In our previous work on supervisory control of discrete event systems, we proposed a novel supervisor which assigns a control pattern based on partial observations of both events and states, and showed necessary and sufficient conditions for its existence. This paper extends the result to decentralized supervisory control of large-scale discrete event systems consisting of several subsystems which operate concurrently. We address two types of decentralized control problems. One requires that the behavior of the closed-loop system equals a given legal language. The other requires that the behavior of the closed-loop system lies in a given admissible range. For each problem, we derive a necessary and sufficient condition for the existence of a decentralized supervisor.

The authors introduce dense real-time into the supervisory control of discrete event systems. They give conditions for the existence of a controller. If the plant and specification behaviors are represented by timed automata, there is a supremal controllable sublanguage of the specification language for a subclass of synthesis problems. The synthesized supervisor is polynomial in the number of automata states and exponential in the timing information. >

In this paper, we investigate the supervisory control of discrete event systems for bisimulation equivalence, in which the plant and the specification are modeled as nondeter-ministic automata. A notion of synchronous simulation-based state controllability is introduced and is shown to be a sufficient condition for the existence of a bisimilarity enforcing supervisor. A polynomial algorithm is developed to check such a condition. When the existence condition holds, a bisimilarity enforcing supervisor is constructed. When the condition does not hold, the synthesis of feasible sub-specifications is further studied.

The supervisory control theory is a general theory for automatic synthesis of controllers (supervisors) for discrete event systems, given a plant model and a specification for the controlled behavior. Though the theory has for over a decade received substantial attention in academics, still very few industrial applications exist. The main reason for this seems to be a discrepancy between the abstract supervisor and its physical implementation. This is specifically noticeable when the implementation is supposed to be based on programmable logic controllers (PLCs), as is the case with many manufacturing systems. The asynchronous event-driven nature of the supervisor is not straightforwardly implemented in the synchronous signal-based PLC. We point out the main problems of supervisor implementation on a PLC, and suggest procedures to alleviate the problems.

This paper surveys recent work of the author with several collaborators, principally Feng Lin, Weilin Wang, and Tae-Sic Yoo; they are kindly acknowledged. Decentralized control of discrete event systems, where local controllers cannot explicitly communicate in real-time, is considered in the first part of the paper. Then the problem of real-time communication among a set of local discrete-event controllers (or diagnosers) is discussed. The writing is descriptive and is meant to inform the reader about important conceptual issues and some recently-completed or on-going research efforts.

In recent years fuzzy sets theory has been widely used in the control of many complex industrial continuous processes. However, there are few researches that have tried to use this theory in the domain of discrete event systems (DESs). In this paper, an approach for modeling and control of a high-speed discrete event system is proposed. This approach consists in the association of a fuzzy controller and a unified formalism based on hybrid Petri nets. The controller consists of a set of local fuzzy controllers which can be linked to a supervisor. Each local fuzzy controller is used to control a specific component of the system. These components are generally multi-inputs single-output processes. The Petri nets model is used to simulate the system and the interactions existing between the system and the controller. >

Standard Petri nets are an untimed logical model. But timing information is important for real‐time control of discrete event systems. This paper studies state feedback control of concurrent discrete event systems modeled by controlled time Petri nets. It is assumed that a control specification is given in terms of markings. A maximal element of the set of controllers achieving a control specification is called a maximally permissive controller (MPC). In general, the MPC is not necessarily unique in controlled time Petri nets. In this paper, we present a necessary and sufficient condition for the unique existence of the maximally permissive controller. Then we derive a closed form expression of the unique MPC if it exists. Moreover, we synthesize a unique MPC for a simple manufacturing system.

This paper studies supervisory control of discrete event systems subject to specifications modeled as nondeterministic automata. The control is exercised so that the controlled system is simulation equivalent to the (nondeterministic) specification. Properties expressed in the universal fragment of the branching-time logic can equivalently be expressed as simulation equivalence specifications. This makes the simulation equivalence a natural choice for behavioral equivalence in many applications and it has found wide applicability in abstraction-based approaches to verification. While simulation equivalence is more general than language equivalence, we show that existence as well as synthesis of both the target and range control problems remain polynomially solvable. Our development shows that the simulation relation is a preorder over automata, with the union and the synchronization of the automata serving as an infimal upperbound and a supremal lowerbound, respectively. For the special case when the plant is deterministic, the notion of state-controllable-similar is introduced as a necessary and sufficient condition for the existence of similarity enforcing supervisor. We also present conditions for the existence of a similarity enforcing supervisor that is deterministic.

In this paper, the problem of designing robust supervisory controllers for uncertain discrete event systems is studied. It is assumed that both the plant behavior and the design specifications can be represented by regular languages. It is also assumed that the unknown model of the uncertain plant belongs to a finite set of possibilities. To solve the problem, a modular approach based on a general recursive robust control scheme is developed. The contribution of the present paper consists in deriving a maximally permissive modular robust supervisory controller for the case of prefix-closed languages, having the advantage of linear complexity in the number of models as opposed to the exponential complexity of the worst-case scenario in the direct implementation of standard supervisors for augmented systems.