Robust and fault-tolerant supervisory control of discrete event systems with partial observation and model uncertainty

This paper proposes the notions of faults and failures in discrete event systems (DESs) with partial observation. They are associated with controllability and an observability property. The proposed notions are used to address the notion of tolerable fault event sequences which represents fault-tolerant behaviour of systems as a desired specification. A robust and fault-tolerant supervisor is a controller which is robust to model uncertainty and guarantees fault-tolerant behaviour of a system. In this paper we present necessary and sufficient conditions for the existence of a robust and fault-tolerant supervisor. The developed conditions capture the concepts of controllability and observability which are cores in the control of DESs with partial observation     

Supervisory control of timed discrete event systems under partial observation based on activity models and eligible time bounds

To avoid the state–space explosion by including tick events in timed discrete event systems (DESs) under partial observation, a notion of eligible time bounds is introduced and based on the notion, controllability and observability conditions of languages are presented. In particular, this paper shows that these controllability and observability conditions are necessary and sufficient for the existence of a supervisor to achieve the given language specification.     

Masked prioritized synchronization for interaction and control of discrete event systems

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 masked 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.     

Control Synthesis of Petri Nets Based on S-Decreases

A method for constructing a controller for a discrete event system modeled by a Petri net is presented in this paper. The control specification of the system is given by a set of linear inequality constraints defined on the marking of the net. The controller that forces the net to obey the constraints is an extended Petri net, which is synthesized based on minimal support S-decreases. The method can deal with general Petri nets with uncontrollable transitions, and then provides a systematic way for synthesizing net-based controllers for discrete event systems.     

Control synthesis of timed discrete event systems based onpredicate invariance

In this paper, arc-timed Petri nets are used to model controlled real-time discrete event systems, and the control synthesis problem that designs a controller for a system to satisfy its given closed-loop behavior specification is addressed. For the problem with the closed-loop behavior specified by a state predicate, real-time control-invariant predicates are introduced, and a fixpoint algorithm to compute the unique extremal control-invariant subpredicate of a given predicate, key to the control synthesis, is presented. For the problem with the behavior specified by a labeled arc-timed Petri net, it is shown that the control synthesis problem can be transformed into one that synthesizes a controller for an induced arc-timed Petri net with a state predicate specification. The problem can then be solved by using the fixpoint algorithm as well. The algorithm involves conjunction and disjunction operations of polyhedral sets and can be algorithmically implemented, making automatic synthesis of controllers for real-time discrete event systems possible.     

Fractional order [proportional derivative] controller for a class of fractional order systems

Recently, fractional order systems (FOS) have attracted more and more attention in various fields. But the control design techniques available for the FOS suffer from the lack of direct systematic approaches. In this paper, we focus on a given type of simple model of FOS. A fractional order [proportional derivative] (FO-[PD]) controller is proposed for this class of FOS, and a practical and systematic tuning procedure has been developed for the proposed FO-[PD] controller synthesis. The fairness issue in comparing with other controllers such as the traditional integer order PID (IO-PID) controller and the fractional order proportional derivative (FO-PD) controller has been addressed under the same number of design parameters and the same specifications. Fair comparisons of the three controllers (i.e., IO-PID, FO-PD and FO-[PD]) via the simulation tests illustrate that, the IO-PID controller designed may not always be stabilizing to achieve flat-phase specification while both FO-PD and FO-[PD] controllers designed are always stabilizing. Furthermore, the proposed FO-[PD] controller outperforms FO-PD controller for the class of fractional order systems.     

On Solvability of a Decentralized Supervisory Control Problem With Communication

We study a decentralized control problem of discrete event systems with communication. We first give a general automata-theoretic formalism that enables us to handle various types of communication, including delay. The decentralized control problem is shown to be undecidable under this formalism. Next we propose a semi-decision procedure for computing finite-state controllers to achieve a given specification in the sense of bisimilarity between the controlled system and a given specification. Using this procedure, we prove decidability of the problem for two special cases, one is the case in which the communication behavior is given as $k$ -bounded-delay communication, and the other is the case in which any cycle in the state transition diagram of the system contains an event observable by all controllers. We also show a method for optimizing controllers based on a graph problem.      

Sampled-data supervisory control

This paper focuses on the issues related to the implementation of theoretical timed discrete-event systems (TDES) supervisors, and the concurrency and timing delay issues involved. In particular, we examine issues related to implementing TDES as sampled-data (SD) controllers. An SD controller is driven by a periodic clock and sees the system as a series of inputs and outputs. On each clock edge (tick event), it samples its inputs, changes state, and updates its outputs. We identify a set of existing TDES properties that will be useful to our work, but not sufficient. We extend the TDES controllability definition to a new definition, SD controllability, which captures several new properties that will be useful in dealing with concurrency issues, as well as make it easier to translate a TDES supervisor into an SD controller. We present controllability and non-blocking results for SD controllers.     

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.     

A behavior-based intelligent control architecture with applicationto coordination of multiple underwater vehicles

Presents a behavior-based intelligent control architecture for designing controllers which, based on their observation of sensor signals, compute the discrete control actions. These control actions then serve as the “set-points” for the lower level controllers. The behavior-based approach yields an intelligent controller which is a cascade of a perceptor and a response controller. The perceptor extracts the relevant symbolic information from the incoming continuous sensor signals, which enables the execution of one of the behaviors. The response controller is a discrete event system that computes the discrete control actions by executing one of the enabled behaviors. The behavioral approach additionally yields a hierarchical two layered response controller, which provides better complexity management. The inputs from the perceptor are used to first compute the higher level activities, called behaviors, and next to compute the corresponding lower level activities, called actions. The paper focuses on the discrete event subsystem, namely, the response controller. We illustrate the intelligent control architecture by discussing its application to the design of intelligent controllers for autonomous underwater vehicles used for ocean sampling missions. A complete set of discrete event models of the response controller of the underwater vehicles for the above application has been given, and their formal verification discussed     

A method for the modular synthesis of controllers for timed discrete-event systems

A method for the modular supervisory control of timed discrete-event systems (TDES) is presented. The modular synthesis method is an extension of the centralized synthesis method proposed in our earlier work. We consider a state predicate specification as a conjunction of several state subpredicate specifications. The control problem is to synthesize a modular controller, the conjunction of all individual controllers, in such a way that the closed-loop behaviour of TDES satisfies the state predicate specification. Our modular synthesis method is developed based on the concept of state space of TDES, the notion of control-invariant state predicates for the TDES and a fixed point algorithm to calculate a control-invariant state subpredicate of a given state predicate. In addition, for the development of our modular synthesis method, we introduce the notion of control-invariance non-conflict among control-invariant state predicates, and the notion of forcing-non-conflict among controllers synthesized based on control-invariant state predicates which are control-invariance non-conflicting. The modular synthesis method in general offers better design flexibility and may require fewer computations than the centralized one. As in our centralized synthesis method, the proposed modular synthesis method does not require the construction and examination of complete sequences of event trajectories of the system. It is suggested that the computation of our proposed method of yielding solutions for a class of synthesis problems in TDES can be economical.     

Optimal Nonblocking Directed Control of Discrete Event Systems

For the control of discrete event systems, the notion of directed control refines that of supervisory control. A directed controller is one that selects at most one controllable event to be enabled at any state (without disabling any uncontrollable event), which is in fact how a discrete event control is implemented. In contrast, a supervisory controller computes a maximal allowable set of controllable events at each state, leaving undecided exactly which controllable event should be enabled. In previous works, we developed a framework for the computation of optimal directed controllers and a polynomial synthesis algorithm for acyclic plants. In this paper, we present a novel synthesis approach for general plants, i.e., plants with or without cycles, thus providing a complete solution to the optimal directed control problem. The complexity of the approach remains polynomial in the size of plant.      

A behavioral approach to the control of discrete linear repetitive processes

This paper formulates the theory of linear discrete time repetitive processes in the setting of behavioral systems theory. A behavioral, latent variable model for repetitive processes is developed and for the physically defined inputs and outputs as manifest variables, a kernel representation of their behavior is determined. Conditions for external stability and controllability of the behavior are then obtained. A sufficient condition for stabilizability is also developed for the behavior and it is shown under a mild restriction that, whenever the repetitive system is stabilizable, a regular constant output feedback stabilizing controller exists. Next, a notion of eigenvalues is defined for the repetitive process under an action of a closed-loop controller. It is then shown how under controllability of the original repetitive process, an arbitrary assignment of eigenvalues for the closed-loop response can be achieved by a constant gain output feedback controller under the above restriction. These results on the existence of constant gain output feedback controllers are among the most striking properties enjoyed by repetitive systems, discovered in this paper. Results of this paper utilize the behavioral model of the repetitive process which is an analogue of the 1D equivalent model of the dynamics studied in earlier work on these processes.     

State feedback control of real-time discrete event systems with infinite states

In this paper, we study a state feedback supervisory control of timed discrete event systems (TDESs) with infinite number of states modelled as timed automata. To this end, we represent a timed automaton with infinite number of untimed states (called locations) by a finite set of conditional assignment statements. Predicates and predicate transformers are employed to finitely represent the behaviour and specification of a TDES with infinite number of locations. In addition, the notion of clock regions in timed automata is used to identify the reachable states of a TDES with an infinite time space. For a real-time specification described as a predicate, we present the controllability condition for the existence of a state feedback supervisor that restricts the behaviour of the controlled TDES within the specification.     

Supervisory control of fuzzy discrete event systems: a formal approach.

Fuzzy discrete event systems (DESs) were proposed recently by Lin and Ying [19], which may better cope with the real-world problems of fuzziness, impreciseness, and subjectivity such as those in biomedicine. As a continuation of [19], in this paper, we further develop fuzzy DESs by dealing with supervisory control of fuzzy DESs. More specifically: 1) we reformulate the parallel composition of crisp DESs, and then define the parallel composition of fuzzy DESs that is equivalent to that in [19]. Max-product and max-min automata for modeling fuzzy DESs are considered, 2) we deal with a number of fundamental problems regarding supervisory control of fuzzy DESs, particularly demonstrate controllability theorem and nonblocking controllability theorem of fuzzy DESs, and thus, present the conditions for the existence of supervisors in fuzzy DESs; 3) we analyze the complexity for presenting a uniform criterion to test the fuzzy controllability condition of fuzzy DESs modeled by max-product automata; in particular, we present in detail a general computing method for checking whether or not the fuzzy controllability condition holds, if max-min automata are used to model fuzzy DESs, and by means of this method we can search for all possible fuzzy states reachable from initial fuzzy state in max-min automata. Also, we introduce the fuzzy n-controllability condition for some practical problems, and 4) a number of examples serving to illustrate the applications of the derived results and methods are described; some basic properties related to supervisory control of fuzzy DESs are investigated. To conclude, some related issues are raised for further consideration.     

DISCRETE OUTPUT FUZZY CONTROLLER DESIGN FOR ACHIEVING COMMON CONTROLLABILITY GRAMIAN

In control theory, the robust properties of linear systems can be related directly to properties of the controllability or observability Gramian. In this paper, a discrete fuzzy controller for a class of nonlinear systems is developed to achieve a common controllability Gramian. We assume that the nonlinear system is represented by the Takagi‐Sugeno fuzzy model. The purpose of this paper is to find the output feedback gains for the T‐S fuzzy controller after assigning a certain common controllability Gramian. Finally, we provide a numerical example to verify the effects of the proposed method.     

Existence and Verification for Decentralized Nondeterministic Discrete‐Event Systems Under Bisimulation Equivalence

In this paper, we study the decentralized control problem for nondeterministic discrete‐event systems (DESs) under bisimulation equivalence. In order to exactly achieve the desired specification in the sense of bisimulation equivalence, we present a synchronous composition for the supervised system based on the simulation relation between the specification and the plant. After introducing the notions of simulation‐based controllability and simulation‐based coobservability, we present the necessary and sufficient condition for the existence of a decentralized supervisor such that the controlled system is bisimilar to the specification, and an algorithm for verifying the simulation‐based coobservability is proposed by constructing a computational tree.     

Supervisory Control of a Class of Concurrent Discrete Event Systems Under Partial Observation

In this paper, we study supervisory control of a class of discrete event systems with simultaneous event occurrences, which we call concurrent discrete event systems, under partial observation. The behavior of the system is described by a language over the simultaneous event set. First, we prove that L_m(G)-closure, controllability, observability, and concurrent well-posedness of a specification language are necessary and sufficient conditions for the existence of a nonblocking supervisor. Next, we synthesize a supervisor that achieves the infimal closed, controllable, observable, and concurrently well-posed superlanguage of a specification language. Finally, we synthesize a supervisor that achieves a maximal closed, controllable, observable, and concurrently well-posed sublanguage of a closed specification language.     

Synthesis of Inference-Based Decentralized Control for Discrete Event Systems

In our past work, we presented a framework for the decentralized control of discrete event systems involving inferencing over ambiguities, about the system state, of various local decision makers. Using the knowledge of the self-ambiguity and those of the others, each local control decision is tagged with a certain ambiguity level (level zero being the minimum and representing no ambiguity). A global control decision is taken to be a "winning" local control decision, i.e., one with a minimum ambiguity level. For the existence of a decentralized supervisor, so that for each controllable event the ambiguity levels of all winning disablement or enablement decisions are bounded by some number N (such a supervisor is termed N-inferring), the notion of N- inference-observability was introduced. When the given specification fails to satisfy the iV-inference-observability property, an iV-inferring supervisor achieving the entire specification does not exist. We first show that the class of iV-inference-observable sublanguages is not closed under union implying that the supremal N- inference-observable sublanguage need not exist. We next provide a technique for synthesizing an N -inferring decentralized supervisor that achieves an N -inference-observable sublanguage of the specification. The sublanguage achieved equals the specification language when the specification itself is iV-inference-observable. A formula for the synthesized sublanguage is also presented. For the special cases of N = 0 and N = 1, the proposed supervisor achieves the same language as those reported in [25], [31] (for N = 0) and [32] (for N = 1). The synthesized supervisor is parameterized by N (the parameter bounding the ambiguity level), and as N is increased, the supervisor becomes strictly more permissive in general. Thus, a user can choose N based on the degree of permissiveness and the degree of computational complexity desired.     

An Iterative Method of the Structural-Parametric Design of Robust Systems with State Controllers

An iterative method for designing a robust control system with state controllers is proposed that includes a transformation of the plant structure to improve its controllability by correcting the singular values of the controllability Gramian and the subsequent synthesis of the basic controller for the corrected plant using modal control. This approach allows us to design systems satisfying the robust stability condition for the given intervals of variation of the plant parameters.