Shigemasa Takai

Inference-Based Ambiguity Management in Decentralized Decision-Making: Decentralized Control of Discrete Event Systems

Decentralized decision-making requires the interaction of various local decision-makers in order to arrive at a global decision. Limited sensing capabilities at each local site can create ambiguities in a decision-making process at each local site. We argue that such ambiguities are of differing gradations. We propose a framework for decentralized decision-making (applied to decentralized control in particular) that allows computation of such ambiguity gradations and utilizes their knowledge in arriving at a global decision. Each local decision is tagged with a certain grade or level of ambiguity, with zero being the minimum ambiguity level. A global decision is taken to be the same as a ldquowinningrdquo local decision, i.e., one having the minimum level of ambiguity. The computation of an ambiguity level for a local decision requires an assessment of the self-ambiguities as well as the ambiguities of the others, and an inference based upon such knowledge. 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 is introduced. We show that the conjunctive-and-permissive (C&P) V disjunctive-and-antipermissive (D&A) co-observability is the same as the zero-inference observability, whereas the conditional C&P V D&A co-observability is the same as the unity-inference observability. We also present examples of higher order inference-observable languages. Our framework does not require the existence of any a priori partition of the controllable events into permissive/antipermissive sets, nor does it require a global control computation based on conjunction/disjunction of local decisions, exhibiting that our ambiguity-based approach is more efficient.

Inference-Based Ambiguity Management in Decentralized Decision-Making: Decentralized Diagnosis of Discrete-Event Systems

The task of decentralized decision-making involves interaction of a set of local decision-makers, each of which operates under limited sensing capabilities and is thus subjected to ambiguity during the process of decision-making. In our prior work, we made a key observation that such ambiguities are of differing gradations and presented a framework for inferencing over varying ambiguity levels to arrive at local and global control decisions. We develop a similar framework for performing diagnosis in a decentralized setting. For each event-trace executed by a system being monitored, each local diagnoser issues its own diagnosis decision (failure or nonfailure or unsure), tagged with a certain ambiguity level (zero being the minimum). A global diagnosis decision is taken to be a ldquowinningrdquo local diagnosis decision, i.e., one with a minimum ambiguity level. The computation of an ambiguity level for a local decision requires an assessment of the self-ambiguity as well as the ambiguities of the others, and an inference based up on such knowledge. In order to characterize the class of systems for which any fault can be detected within a uniformly bounded number of steps (or ldquodelayrdquo), we introduce the notion of N -inference-diagnosability for Failures (also called N-inference F-diagnosability), where the index N represents the maximum ambiguity level of any winning local decision. We show that the codiagnosability introduced in is the same as 0-inference F-diagnosability; the conditional F-codiagnosability introduced in , is a type of 1-inference F-diagnosability; the class of higher-index inference F-diagnosable systems strictly subsumes the class of lower-index ones; and the class of inference F-diagnosable systems is strictly subsumed by the class of systems that are centrally F-diagnosable.

Decentralized Prognosis of Failures in Discrete Event Systems

We study the prognosis of failures, i.e., their prediction prior to their occurrence, in discrete event systems in a decentralized setting where multiple prognosers use their local observations to issue local prognosis decisions. We define the notion of correctness of a decentralized set of prognosers in terms of ?no missed detections? (each failure is prognosed prior to its occurrence) and ?no false alarms? (an incorrect prognostic decision is never issued), and introduce the notion of coprognosability as an existence condition. When specialized to the centralized case (i.e., the case of a single prognoser), this condition turns out to be weaker than the one introduced by Genc and Lafortune in 2006 since a uniform bound on the number of steps within which a failure will occur is not required. For comparison, we also introduce the stronger notion of ?uniformly bounded coprognosability? and identify the subclass of decentralized prognosers for which it serves as an existence condition. We show that the two notions coincide when the underlying system and its nonfailure specification possess finite-state representations, and present a verification algorithm whose complexity is polynomial in the sizes of the system being prognosed and its nonfailure specification, and is exponential in the number of the local prognosers. We also introduce the notion of reaction bound for coprognosis as the earliest time beyond a prognostic decision when a failure can occur, and present an algorithm for computing it. The complexity of this algorithm is identical to that of the verification algorithm. An algorithm with complexity linear in the size of the specification and the number of local prognosers is also presented for an online prognosis of failures. We show that the notions of coprognosability and its uniformly bounded version are in general incomparable with the notion of codiagnosability (that guarantees a uniformly bounded delay detection of a failure by a local diagnoser). When the system cannot execute an unbounded sequence of unobservable events, uniformly bounded coprognosability implies codiagnosability, whereas coprognosability and codiagnosability remain incomparable.

Effective computation of an Lm(G)-closed, controllable, and observable sublanguage arising in supervisory control

Abstract In this paper, we study nonblocking supervisory control of discrete event systems under partial observation. A nonblocking supervisor can be synthesized for the supremal L m ( G )-closed, controllable, and normal sublanguage of a given (nonclosed) marked language. However, such a supervisor may be too restrictive as a solution to the supervisory control problem. We identify a subclass of observable sublanguages of a given language, which has the supremal element larger than the supremal normal sublanguage. By using the supremal element, we present an iterative algorithm for computing an L m ( G )-closed, controllable, and observable sublanguage of a given marked language, which is larger than the supremal L m ( G )-closed, controllable, and normal sublanguage.

Robust supervisory control of a class of timed discrete event systems under partial observation

This paper studies robust supervisory control of timed discrete event systems proposed by Brandin and Wonham. Given a set of possible models which includes the exact model of the plant, the objective is to synthesize a robust supervisor such that it achieves legal behavior for all possible models. We show that controllability for each possible model and observability for a suitably defined aggregate model are necessary and sufficient conditions for the existence of a solution to the robust supervisory control problem. Moreover, when there does not exist a solution, a maximally permissive robust supervisor is synthesized under the assumption that all controllable events are observable.

Decentralized state feedback control of discrete event systems

Abstract In this paper, we consider decentralized state feedback control of discrete event systems with a (global) control specification given by a predicate. In this framework, instead of a global state feedback, each local state feedback controls a part of the system according to local information so that global behaviors satisfy the global control specification. We introduce the notion of n- observability of predicates, and present necessary and sufficient conditions for the existence of a decentralized state feedback which achieves the global control specification.

On the language generated under fully decentralized supervision

This paper studies the language generated under fully decentralized supervision proposed by Kozak and Wonham (1995). The author assumes that desirable behavior is specified as a closed language. A closed-form expression for the language generated under fully decentralized supervision is presented. It is shown that the generated language is larger than the supremal closed, controllable, and strongly decomposable sublanguage. Moreover, a necessary and sufficient condition is derived for the generated language to be the supremal closed and controllable sublanguage.

Inference-based decentralized prognosis in discrete event systems

For discrete event systems, we study the problem of predicting failures prior to their occurrence, also referred to as prognosis, in the inference-based decentralized framework where multiple decision-makers interact to come up with the global prognostic decisions. Due to the limited sensing capabilities, each decision-maker is subjected to ambiguities during the process of decision-making. In our prior work we made an observation that such ambiguities are of differing gradations and presented a framework for inferencing over the local control decisions of varying ambiguity levels to arrive at a global control decision. Here we present an inference-based decentralized decision-making framework for prognosis of failures: For each event-trace executed by a system being monitored, each local prognoser issues its own prognostic decision (failure is or is not inevitable, or unsure) tagged with a certain ambiguity level (zero being the minimum) that is computed by assessing the ambiguities of the self and the others. A global prognostic decision is taken to be the ?winning? local prognostic decision, i.e., one with the minimum ambiguity level. We characterize the class of systems for which there are no missed detections (all failures can be prognosed prior to their occurrence) and no false alarms (all prognostic decisions are correct) by introducing the notion of N-inference-prognosability, where the parameter N represents the maximum ambiguity level of any winning prognostic decision. An algorithm for verifying N-inference-prognosability is presented. We also show that the notion of coprognosability introduced is the same as 0-inference-prognosability, and as the parameter N is increased, a larger class of prognosable systems is obtained.

Verification and synthesis for secrecy in discrete-event systems

Keeping a property of system behaviors secret from an observer (who has a partial observation of any executed behavior) requires that the execution of any property-satisfying or property-violating behavior must not become known to the observer. When an observer does not know the exact behaviors of a system it observes, a weaker notion of secrecy can be defined, which we introduce in this paper. We present an algorithm for verifying the properties of secrecy as well as its weaker version. When a given system does not possess a secrecy property, we consider restricting the behaviors of the system by means of supervisory control so as to ensure that the controlled system satisfies the desired secrecy property. We show the existence of a maximally permissive supervisor to ensure secrecy or its weaker version, and present algorithms for their synthesis.

Characterization of co-observable languages and formulas for their super/sublanguages

We present fixed-point based characterization of several classes of co-observable languages that are of interest in the context of decentralized supervisory control of discrete-event systems, including C&P /spl or/ D&A co-observable languages, C&P co-observable languages, and D&A co-observable languages. We also provide formulas for computing super/sublanguages for each of these classes. In cases where the class of co-observable languages is not closed under intersection/union, we provide upper/lower bound of the super/sublanguage formula we present. The computation of super/sublanguages and also computation of their upper/lower bounds has lead to the introduction of other classes of co-observable languages, namely, strongly C&P co-observable languages, strongly D&A co-observable languages, locally observable languages, and strongly locally observable languages. Fixed-point based characterization of all the above language classes is also given, and their closure under intersection/union is investigated. We also study whether the fixed-point operator preserves prefix closure, relative closure (also called L/sub m/(G)-closure), and controllability.