Optimization-based computation of bounded sequences to reach target states in DESs

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.

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.

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.

The supervisory control theory of discrete event systems modeled as finite state machines (FSMs) have been studied for many years. However, the problem of state explosion in the existing theories obstructs its widespread application. To alleviate the problem, extended finite state machines (EFSMs) are considered to model discrete event systems. In the theories of supervisory control of discrete event systems, controllability is very important. So the controllability of EFSM is vital to study the supervisory control problem of discrete event systems modeled as EFSMs. This paper focuses on the controllability of EFSMs. Firstly, the controllability of EFSM is proposed. Secondly, based on the definition of non-cyclic path and EFSM of deleting-configurations, the necessary and sufficient condition for controllability and an algorithm for deciding controllability are presented.KeywordsInitial ConfigurationFinite State MachineSupervisory ControlState ExplosionCyclic PathThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Modeling and control of discrete event systems using finite state machines with variables and their applications in power grids

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.

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.

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.

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 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. >

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.

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.

In the paper, we study the supervisory control (event string avoidance control) of discrete event systems (DES's) of which the physical possible behavior is modelled by an ordinary Petri net and legal behavior is specified by a deterministic labelled Petri net. The advantage of taking a Petri net as the specification of the legal behavior of a DES is that it can both specify the desired interleaving behavior and the concurrent execution constraints of the DES. The problem of the paper is to synthesize a feedback control policy for a DES such that the behavior of the DES under the control of the control policy satisfies a given behavior specification. To solve the problem, we first transform it into an equivalent state feedback control (state avoidance control) problem of an induced system with specific permissive state set. For the permissive state set, under a weak assumption that the underlying system can not occur any infinite uncontrollable event sequence, we propose a method to calculate the supremal control-invariant subset of the permissive state set, and then give a minimally restrictive state feedback control policy allowing maximal concurrency for the induced system. >

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.