Robust supervisory control of timed discrete event systems under partial observation based on eligible time bounds: The existence conditions

This paper addresses a supervisory control problem for uncertain timed discrete event systems (DESs) under partial observation. An uncertain timed DES to be controlled is represented by a set of possible timed models based on the framework of Brandin and Wonham [(1994). Supervisory control of timed discrete event systems. IEEE Transactions on Automatic Control, 39(2), 329-342]. To avoid the state space explosion problem caused by tick events in the timed models, a notion of eligible time bounds is proposed for a single timed model obtained from the set of all possible timed models. Based on this notion, we present the necessary and sufficient conditions for the existence of a robust supervisor achieving a given language specification for the single timed model. Moreover, we show that the robust supervisor can also achieve the specification for any timed model in the set.     

Robust and nonblocking supervisory control of nondeterministicdiscrete event systems using trajectory models

This note considers the robust supervisory control problems of uncertain nondeterministic discrete-event systems (DESs). The uncertain DES to be controlled is assumed to be modeled as a set of some possible nondeterministic automata. Then, the control objective is to achieve a given language specification and guarantee the nonblockingness of any nondeterministic automata of the set which are controlled by a robust nonblocking supervisor. Based on trajectory models, this note presents the necessary and sufficient conditions for the existence of a robust nonblocking supervisor for a given uncertain nondeterministic DES     

Robust and adaptive supervisory control of discrete event systems

Both robust and adaptive supervisory control in discrete-event systems are discussed. It is assumed that the system G to be controlled is not known exactly. It is only known either that it belongs to a set or that it has certain lower and upper bounds. The task of robust supervision is to synthesize a supervisor that realizes a given desired behavior for all possible G. A necessary and sufficient condition for the existence of such a robust supervisor is derived. Based on this condition, a robust supervisory control and observation problem of synthesizing a robust supervisor whose behavior is both legal and acceptable is solved. Adaptive supervision is discussed. As the system progresses, the information on occurrences of events may help to resolve or reduce uncertainties     

Robust nonblocking supervisory control of discrete-event systems

In this note, we generalize a robust supervisory control framework to deal with marked languages. We show how to synthesize a supervisor to control a family of plant models, each with its own specification. The solution we obtain is the most general in that it provides the closest approximation to the supremal controllable sublanguage for each plant/specification pair. We end the note by extending these results to deal with timed discrete-event systems.     

Decentralized supervisory control of nondeterministic discrete event systems: The existence condition of a robust and nonblocking supervisor

This paper addresses a decentralized supervisory control problem for an uncertain discrete event system (DES) modeled by a set of possible nondeterministic automata with unidentified internal events. For a given language specification, we present the existence condition of a robust and nonblocking decentralized supervisor that achieves this specification for any nondeterministic model in the set. In particular, we show that the given language specification can be achieved based on the properties of its controllability and coobservability with respect to the overall nominal behavior of the uncertain DES. It is further shown that the existence of a nonblocking decentralized supervisor can be examined with a trajectory model of the language specification.     

Maximizing robustness of supervisors for partially observed discrete event systems

We consider a robust supervisory control problem to synthesize a supervisor for the nominal plant model which maximizes robustness. Cury and Krogh have first addressed this problem by unnecessarily restricting the upper bound of the legal behavior. In our previous work, we have solved the problem without restricting the upper bound of the legal behavior when the specification is described by prefix-closed languages. In this paper, we extend our previous work to the partial (event) observation case. First, we synthesize a supervisor that maximizes robustness. This result shows that robustness can be optimized under partial observation, while permissiveness cannot be optimized in general. We next consider a special case where all the controllable events are observable. In this special case, we synthesize a maximally permissive supervisor for the nominal plant model which maximizes not only the robustness but also permissiveness for the maximal set of admissible plant variations.     

Robust nonblocking supervisory control of discrete-event systems under partial observation

In this paper, we examine the problem of robust nonblocking supervisory control. In the problem considered here, the exact model of the plant is not known but is assumed to be among a finite set of possible models. For each plant model a legal marked behavior is assumed given. We extend previous results for the case of control with full observation to the case of control under partial observation where only a subset of events are observable. Furthermore, we remove the limitations of previous results on ensuring the nonblocking property of the plant under supervision. We characterize the entire set of solutions of the robust control problem and obtain a set of necessary and sufficient conditions for the existence of a solution for the problem. As an illustrative example, we use our results on robust control to solve a fault recovery problem.     

On the existence of supervisory policies that enforce liveness indiscrete-event dynamic systems modeled by controlled Petri nets

We consider discrete-state plants represented by controlled Petri nets (CtlPNs), where a subset of transitions can be prevented from firing by a supervisor. A transition in a CtlPN can fire at a marking if there are sufficient tokens in its input places and it is permitted to fire by the supervisor. A CtlPN is live if it is possible to fire any transition from every marking that is reachable under supervision. In this paper we derive a necessary and sufficient condition for the existence of a supervisory policy that enforces liveness in CtlPNs. We show this condition cannot be tested for an arbitrary CtlPN. However, for bounded CtlPNs or CtlPNs, where each transition is individually controllable, we show the existence of a supervisory policy which enforces that liveness is decidable. We also show the existence of a supervisory policy that enforces liveness is necessary and sufficient for the existence of a minimally restrictive supervisory policy     

Supervisory multiple regime control

The objective of this work is to identify a control algorithm that is capable of handling nonlinear behaviour (operating point dependent) witnessed in most industrial processes. To this end, the proposed solution is that of a supervisory multiple model control scheme, SMMC. This work demonstrates that the multiple model methodology can be recast into a Supervisory approach, whereby the supervisor is employed as a selector. This selector (supervisor) identifies the appropriate local-controller from a fixed family set. Unlike other supervisory techniques a multiple model observer (MMO) is proposed for the selection mechanism. Switching between local-controllers is accomplished bumplessly through a multiple model bumpless transfer scheme. Consequently, producing a continuous control signal as the process transverses between different operating regimes. The key issue in this application is the unique interaction between the local-controllers and the supervisor. This interaction is necessary to ensure global stability is maintained at all times, especially during switching. In short, the SMMC scheme enables the implementation of linear control theory, which is well accepted in industry, to standard nonlinear processes. The SMMC approach warrants the control design to extend beyond normal operating conditions that breakdown when standard linear control techniques are applied. The above notion is applied to a pilot-scale binary distillation column. In this example the column's distinct operating points describe the nonlinear behaviour. The results illustrate that as the distillation column shifted between different operating points the SMMC self-regulates accordingly. This self-regulation ensures that global stability and performance are maintained at an optimum. The entire SMMC design was implemented within a PC Windows-NT environment that was interfaced to an industrial DCS system.     

Process objects/masked composition: an object-oriented approach formodeling and control of discrete-event systems

An object oriented framework for modeling and supervisory control of discrete-event systems is described. Control and observation masks are encapsulated with process logic to form process objects, and a single type of interconnection operator called masked composition is used to build complex process objects out of simpler component process objects. The approach applies to both deterministic and nondeterministic plant models and supervisory design. In addition to the usual benefits of object-oriented design, such as software reusability, it yields conditions under which the existence of a nondeterministic supervisor implies existence of a deterministic supervisor     

Reliable decentralized supervisory control of discrete eventsystems

We consider a discrete event system controlled by a decentralized supervisor consisting of n local supervisors, and formulate a new decentralized supervisory control problem, called a reliable decentralized supervisory control problem. A decentralized supervisor is said to be k-reliable (1相似文献   

Control of nondeterministic discrete-event systems for bisimulation equivalence

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.     

Robust and nonblocking supervisor for discrete-event systems withmodel uncertainty under partial observation

Addresses a robust and nonblocking supervisory control problem based on a framework of discrete-event systems with model uncertainty under partial observation. The uncertainty introduced in the paper is associated with internal and unobservable events occurring in systems. The paper presents a systematic method for modeling uncertainty described as a Δ-transition representing the internal and unobservable events. In particular, at a state with the assigned positive integer value p a system is assumed to experience at most a p-step state transition by the internal and unobservable event. Under the framework for model uncertainty, the paper presents necessary and sufficient conditions for the existence of a robust supervisor with the nonblocking property     

On Petri net models of infinite state supervisors

A class of supervisory control problems that require infinite state supervisors is considered, and Petri nets with inhibitor arcs (PNs) are introduced to model the supervisors. This PN-based approach to supervisory control is compared to automata-based approaches. The primary advantage of a PN-based supervisory controller is that it provides a finite representation of an infinite state supervisor. For verification, implementation, and testing reasons, a finite PN-based representation of an infinite state supervisor is preferred over an automata-based supervisor. It is shown that this modeling advantage is accompanied by a decision disadvantage, in that in general the controllability of a language that can be generated by the closed-loop system is undecidable     

Design of Optimal Petri Net Supervisors for Flexible Manufacturing Systems via Weighted Inhibitor Arcs

This paper develops an approach to the design of an optimal Petri net supervisor that enforces liveness to flexible manufacturing systems. The supervisor contains a set of observer places with weighted inhibitor arcs. An observer place with a weighted inhibitor arc is used to forbid a net from yielding an illegal marking by inhibiting the firing of a transition at a marking while ensuring that all legal markings are preserved. A marking reduction technique is presented to decrease the number of considered markings, which can dramatically lower the computational burden of the proposed approach. An integer linear program is presented to simplify the supervisory structure by minimizing the number of observer places. Finally, several examples are used to shed light on the proposed approach which can lead to an optimal supervisor for the net models that cannot be optimally controlled via pure Petri net supervisors.     

Robust Supervisory Control for Product Routings With Multiple Unreliable Resources

Manufacturing systems are often subject to resource failure. In past work, we developed ldquorobustrdquo supervisory controllers for the single-unit resource allocation model. These guarantee that if any subset of resources fail, parts in the system requiring failed resources do not block the production of parts not requiring failed resources. To establish supervisor correctness, we assumed that each part type required at most one unreliable resource in its route. We now relax this assumption using a central buffer and present supervisors that guarantee robust operation without assumptions on route structure.     

Control of Non-Deterministic Systems With μ-Calculus Specifications Using Quotienting

The supervisory control problem for discrete event system(DES) under control involves identifying the supervisor, if one exists, which, when synchronously composed with the DES,results in a system that conforms to the control specification. In this context, we consider a non-deterministic DES under complete observation and control specification expressed in action-based propositional μ-calculus. The key to our solution is the process of quotienting the control specification against the plan resulting in a new μ-calculus formula such that a model for the formula is the supervisor. Thus the task of control synthesis is reduced a problem of μ-calculus satisfiability. In contrast to the existing μ-calculus quotienting-based techniques that are developed in deterministic setting, our quotienting rules can handle nondeterminism in the plant models. Another distinguishing feature of our technique is that while existing techniques use a separate μ-calculus formula to describe the controllability constraint(that uncontrollable events of plants are never disabled by a supervisor), we absorb this constraint as part of quotienting which allows us to directly capture more general state-dependent controllability constraints. Finally, we develop a tableau-based technique for verifying satisfiability of quotiented formula and model generation. The runtime for the technique is exponential in terms of the size of the plan and the control specification. A better complexity result that is polynomial to plant size and exponential to specification size is obtained when the controllability property is state-independent. A prototype implementation in a tabled logic programming language as well as some experimental results are presented.     

A dynamic fuzzy cognitive map applied to chemical process supervision

This work develops an intelligent tool based on fuzzy cognitive maps to supervisory process control. Fuzzy cognitive maps are a neuro-fuzzy methodology that can accurate model complexly system using a causal-effect fuzzy reasoning. In the proposed approach, new types of concept and relation, not restricted to cause–effect ones, are added to the model resulting in a dynamic fuzzy cognitive map (D-FCM). In this sense, a supervisory system is developed in order to control a fermentation process. This process has a non-linear behavior and presents several problems, such as non-minimum phase and large accommodation time. The supervisor goal is to operate the process in normal and critical conditions. The expert knowledge about the process behavior in both conditions is used to build the D-FCM supervisor. Simulation results are presented in order to validate the proposed intelligent supervisor.     

Synthesis of maximally permissive and robust supervisors forprefix-closed language specifications

J.E.R. Cury and B.H. Krogh (1999) have formulated a robust supervisory control problem to synthesize a supervisor for the nominal plant which maximizes robustness. They have solved the problem by unnecessarily restricting the upper bound of the legal behavior. We show that the problem can be solved without restricting the upper bound of the legal behavior when the specification is described by prefix-closed languages. We synthesize a maximally permissive supervisor for the nominal plant which maximizes not only robustness, but also permissiveness for the maximal set of admissible plant variations     

Fully decentralized solutions of supervisory control problems

The paper gives a new characterization of solutions of the decentralized supervisory control problem and presents a special class of “fully decentralized” solutions, so called because the main idea is to avoid communication not only among subsupervisors during run-time but also among agents designing the subsupervisors. The solutions are constructed from optimal centralized ones using a worst-case philosophy. Their basic properties and comparison with the partially observable supervisory control problem are given. If it is known a priori that the fully decentralized solution exists, then the supervisor can be computed partly online. A sufficiency test of the existence of such a solution is provided