Problem solving in control of discrete-event systems

We develop a process-theoretic approach for generally-dis-tributed discrete-event systems with unrestricted nondeterminism that is geared towards supervisory control. Supervisory control theory deals with synthesis of models of supervisory controllers that ensure safe and nonblocking behavior of the supervised system. The models are synthesized based on a model of the uncontrolled system and a formalization of the control requirements. Even though there exist extensions of supervisory control theory for timed and Markovian discrete-event systems, there are hardly any investigations of supervisory control of discrete-event systems with generally-distributed delays. General distributions provide for (convenient) modeling of important real-world phenomena that cannot be consistently modeled by means of real time or Markovian (exponentially-distributed) delays, like heavy-tail or uniformly distributed processes. Our theory relies on a behavioral preorder termed partial bisimulation, for which we provide a suitable extension. Based on the proposed theory we provide for an appropriate abstraction of the stochastic behavior, which enables us to employ standard supervisory controller synthesis tools. The synthesized supervisor can, thereafter, be coupled with the stochastic model of the unsupervised system and abstracted to a generalized semi-Markov process for the purpose of analysis and simulation.

This paper proposes a solution to the electric Vehicle Scheduling Problem (eVSP) based on the framework of Discrete Event System (DES). A supervisory control is synthesized using the theory of Supervisory Control of Discrete Event System (SCDES) to manage the power admission control of a group of local Plug-in Electric Vehicles (PEV). The PEVs are categorized based on their level of priority to be charged and an algorithm is developed to allocate power to PEVs according to their priority and available capacity. The proposed algorithm and supervisor validates the schedulability of charging of PEVs while meeting the constraint of the grid to achieve peak demand reduction. Simulation studies are carried out using MATLAB/Simulink and STATEFLOW toolkit and the result validates the effectiveness of the control scheme to reduce peak demand while providing fair charging schedules to PEVs.

The signed real measure of regular languages has been introduced and validated in recent literature for quantitative analysis and synthesis of discrete-event supervisory (DES) control systems, where all events are assumed to be observable. This paper presents a modification of the language measure for supervisory control under partial observation and shows how to generalize the analysis when some of the events may not be observable at the supervisory level. Thus, for synthesis of DES control systems, the language measure of partially observable discrete-event processes is expressed in a closed form, which is structurally similar to that of completely observable discrete-event processes.

Supervisory control of discrete-event systems: A brief history

As railway platforms expand in size, complexity, and traffic volume, ensuring efficiency and safety of train entrance and exit a station becomes increasingly critical. This study presents a scheduling approach for monorail one-way stations that minimises reliance on the train timetable while validating scheduling decisions against it, thereby enhancing the feasibility and safety of the scheduling process. For multi-platform stations, where switches are organised into partial binary trees, this paper introduces a modular discrete event system (DES) modelling approach to design and implement train entrance and exit schedules. The fundamental modelling unit of a multi-platform station consists of a single module, comprising an entrance/exit switch and its associated sensors. The complete DES model of the train station is then constructed as the synchronous product of multiple such modular units. In addressing train scheduling, the proposed approach incorporates fair train entrance/exit specifications, platform capacity constraints, and crossover capacity limitations. Through the supervisory control of DES, an optimal supervisor is synthesised to prevent collision incidents. This innovative methodology and accompanying algorithm facilitate seamless and equitable scheduling for train entrances and exits, without distinguishing between individual trains traversing the station.

We introduce a framework for fault-tolerant supervisory control of discrete-event systems. Given a plant, possessing both faulty and nonfaulty behavior, and a submodel for just the nonfaulty part, the goal of fault-tolerant supervisory control is to enforce a certain specification for the nonfaulty plant and another (perhaps more liberal) specification for the overall plant, and further to ensure that the plant recovers from any fault within a bounded delay so that following the recovery the system state is equivalent to a nonfaulty state (as if no fault ever happened). The specification for the overall plant is more liberal compared to the one for the nonfaulty part since a degraded performance may be allowed after a fault has occurred. We formulate this notion of fault-tolerant supervisory control and provide a necessary and sufficient condition for the existence of such a supervisor. The condition involves the usual notions of controllability, observability and relative-closure, together with the notion of stability. An example of a power system is provided to illustrate the framework. We also propose a weaker notion of fault-tolerance where following the recovery, the system state is simulated by some nonfaulty state, i.e., behaviors following the recovery are also the behaviors from some faulty state. Also, we formulate the corresponding notion of weakly fault-tolerant supervisory control and present a necessary and sufficient condition (involving the notion of language-stability) for the its existence. We also introduce the notion of nonuniformly-bounded fault-tolerance (and its weak version) where the delay-bound for recovery is not uniformly bounded over the set of faulty traces, and show that when the plant model has finitely many states, this more general notion of fault-tolerance coincides with the one in which the delay-bound for recovery is uniformly bounded.

In the context of supervisory control of discrete-event systems, decentralized control is a well-established area of research. In this paper we present an implementation of such controllers for an assembly cell with two-assembly stations (SCARA robots), in a laboratory scale computer integrated manufacturing (CIM) system. Step by step implementation, conflict avoidance between local supervisors and difficulties encountered are discussed. Petri nets are used as the modelling tool and Lin and Wonham framework is used as the control architecture. Assembly stations are modelled as intelligent agents. A separate software module called order processing module (OPM) is used to handle orders into and out of the system and to schedule the two-assembly stations

We consider a multi-adversary version of the supervisory control problem for discrete-event systems (DES), in which an adversary corrupts the observations available to the supervisor. The supervisor’s goal is to enforce a specific language in spite of the opponent’s actions and without knowing which adversary it is playing against. This problem is motivated by applications to computer security in which a cyber defense system must make decisions based on reports from sensors that may have been tampered with by an attacker. We start by showing that the problem has a solution if and only if the desired language is controllable (in the DES classical sense) and observable in a (novel) sense that takes the adversaries into account. For the particular case of attacks that insert symbols into or remove symbols from the sequence of sensor outputs, we show that testing the existence of a supervisor and building the supervisor can be done using tools developed for the classical DES supervisory control problem, by considering a family of automata with modified output maps, but without expanding the size of the state space and without incurring on exponential complexity on the number of attacks considered.

The aim of this essay is to provide a brief introduction to supervisory control theory of discrete-event systems.

In this paper we develop a data-driven approach for supervisory control of discrete-event systems (DES). We consider a setup in which models of DES to be controlled are unknown, but a set of data concerning the behaviors of DES is available. We propose a new concept of data-informativity, which captures the notion that the available data set contains sufficient information such that a valid supervisor may be constructed for a family of DES models that all can generate the data set. We then characterize data-informativity with a necessary and sufficient condition, based on which we design an algorithm for its verification.

Deterministic supervisory control with flexible upper-bounds on observation delay and control delay

In this paper a hybrid approach is proposed for supervisory control of discrete event systems (DES) subject to forbidden states. Assuming that an uncontrolled bounded Petri net (PN) model of a (plant) DES and a set of forbidden state specifications are given, the proposed approach computes a maximally permissive and nonblocking closed-loop hybrid model. The first step is to simplify the given PN model by means of PN reduction rules. The simplified model and the specifications are then represented as buffers, and supervisory control theory (SCT) is applied to obtain a Ramadge–Wonham (RW) supervisor in the form of an automaton. After reduction of the latter’s state size by a ‘control congruence’, the simplified RW supervisor is represented by a so-called auto-net and coupled to the given uncontrolled PN plant model by means of inhibitor arcs to represent the disabling actions. The plant model and supervisor auto-net run concurrently, synchronizing on shared events. This procedure provides a maximally permissive and nonblocking ‘hybrid’ (mixed PN/automaton) closed-loop controlled system. The method is straightforward logically, graphically, and technologically. Its applicability is shown by two examples, one of them a workcell from the PN control literature.

Eight mountaineers were placed in a hypobaric chamber to simulate oxygen depletion accompanying a mountain ascent. The aim was to examine the evolution of individual and group efficiency in problem solving and anxiety according to simulated altitude. Relationships within the group, state and trait anxiety, and individual and collective performance in problem solving were repeatedly assessed at simulated altitudes of 5000m, 6000m, 7000m, and 8000m. The decrease of individual performance in problem solving, shown to be simultaneous to the increase of state anxiety, had little effect on collective performance in problem solving. These results suggest (a) that the collective success could be due to the emergence of a positive common goal and a positive appraisal of the situation and (b) that the state anxiety could act as a mediator between the variation in altitude and its effects on individual performance. The relevance of these results to real mountaineering expeditions is discussed.

Supervisory control of discrete event systems under asynchronous spiking neuron P systems

Distributed supervisory control is a method to synthesize local controllers in discrete-eventsystems with a systematic observation of the plant. Some works were reported on extending this methodby which local controllers are constructed so that observation properties are preserved from monolithic todistributed supervisory control, in an up-down approach. In this paper, we find circumstances in whichobservation properties are preserved from monolithic to distributed supervisory control. Local observationproperties, i.e. local normality and local relative observability are employed for investigating observationproperties of each local controller, which are constructed by any localization algorithm that preserves controlequivalency to the monolithic supervisor with respect to the plant. These properties enable us to investigatethe observation properties from monolithic to distributed supervisory control. Moreover, observationequivalence property is defined according to the control equivalence in a distributed supervisory controlwith partial observation. It is proved that with preserving observation equivalence of the local controllers tothe monolithic supervisor, the control equivalence is satisfied, if and only if the intersection of local eventsets is a subset of or equal to the global observable event set.