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

We consider a reliable decentralized supervisory control problem for discrete event systems in the conditional architecture. This reliable decentralized control problem requires synthesizing local supervisors such that a given specification can be achieved without blocking even if local control decisions of some local supervisors are not available for making the global control decision. We introduce a notion of reliable conditional-coobservability and show that reliable conditional-coobservability together with reliable controllability and L m (G)-closedness is a necessary and sufficient condition for the existence of a solution to the reliable decentralized control problem. In addition, we develop a method for verifying reliable conditional-coobservability.

A distributed detection system consisting of a number of local detectors and a fusion center is considered. Each detector makes a decision for the underlying binary hypothesis testing problem based on its own observations and transmits its decision to the fusion center where the global decision is derived. The local decision rules are assumed to be given, but the local decisions are correlated. The correlation model is expressed by a finite number of conditional probabilities. The optimum decision fusion rule in the Neyman-Pearson sense is derived and analyzed. The performance of the distributed detection system versus the degree of correlation between the local decisions is studied for a special correlation structure that can be indexed by a single parameter. It is shown that system performance degrades as the degree of correlation between local decisions increases.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

We consider a parallel decentralized detection system employing a bank of local detectors (LDs) to access a commonly-observed phenomenon. The system makes a binary decision about the phenomenon, accepting one of two hypotheses (H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> (“absent” ) or H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> (“present” )). The kth LD uses a local decision rule to compress its local observations y <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> into a binary local decision u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> ; u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> =0 if the kth LD accepts H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> and u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> = 1 accepts H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> . The kth LD sends its decision u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> over a noiseless dedicated channel to a Data Fusion Center (DFC). The DFC combines the local decisions it receives from n LDs (u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> ,u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ,...,u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> ) into a single binary global decision u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> (u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0=</sub> 0 for accepting H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> or u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> =1 for accepting H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> ). If each LD uses a single deterministic local decision rule (calculating u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> from the local observations y <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> ) and the DFC uses a single deterministic global decision rule (calculating u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> from n local decisions), the team receiver operating characteristic (ROC) curve is in general non-concave. The system's performance under a Neyman-Pearson criterion may then be suboptimal in the sense that a mixed strategy may yield a higher probability of detection when the probability of false alarm is constrained not to exceed a certain value, α>0. Specifically, a “dependent randomization” detection scheme can be applied in certain circumstances to improve the system's performance by making the ROC curve concave. This scheme requires a coordinated and synchronized action between the DFC and the LDs. In this study, we specify when dependent randomization is needed, and discuss the proper response of the detection system if synchronization between the LDs and the DFC is temporarily lost.

In a parallel distributed detection system each local detector makes a decision based on its own observations and transmits its local decision to a fusion center, where a global decision is made. Given fixed local decision rules, in order to design the optimal fusion rule, the fusion center needs to have perfect knowledge of the performance of the local detectors as well as the prior probabilities of the hypotheses. Such knowledge is not available in most practical cases. We propose a blind technique for the M-ary distributed detection problem. The occurrence number of a possible decision combination at all local detectors is multinomially distributed with the occurrence probability being a nonlinear function of the prior probabilities of hypotheses and the parameters describing the performance of local detectors. We derive least squares (LS) and maximum likelihood (ML) estimates of unknown parameters using local decisions and compare their individual performance. We also derive analytically the overall detection performance for both binary and M-ary distributed detection and discuss the difference of the overall detection performance obtained using the estimated values of unknown parameters and their true values. Finally, we demonstrate the applicability of our results through numerical examples.

We have previously introduced an inference-based framework for decentralized decision-making, comprising of multiple observers, each with its own partial observation, where inferencing over the ambiguities of the self and the others is used to issue local decisions, and a global decision is taken to be the one possessing the minimum ambiguity level. In this setting, we previously introduced the notion of $N$ -inference $\vee$ -diagnosability to characterize the existence of a disjunctive decentralized diagnosis scheme so that any fault can be detected within a bounded delay, using at most $N$ -levels of inferencing, by one of the diagnosers. While the disjunctive scheme relies on one of the diagnosers making the failure decision , the dual conjunctive scheme relies on none of the diagnosers making the nonfailure decision . It is known that the two schemes are incomparable, and in this paper we extend our earlier work to provide a more general framework, introducing the notion of $N$ -inference diagnosability, capturing both disjunctive and conjunctive schemes. We also develop a method for verifying $N$ -inference diagnosability, as well as discuss several of its useful properties.

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.

Human decision makers think categorically when facing a great variety of objects due to their limited information processing capacities. The categorical thinking by Bayesian decision makers is modeled as classifying objects into a small number of categories with respect to their prior probabilities. The classification follows a quantization rule for the prior probabilities. The categorical thinking enables decision makers to handle infinitely many objects but simultaneously causes them to lose precision of prior probabilities and, consequently, of decisions. This chapter considers group decision making by imperfect agents that only knowquantized prior probabilities for use in Bayesian likelihood ratio tests. Global decisions are made by information fusion of local decisions, but information sharing among agents before local decision making is forbidden. The quantization rule of the agents is investigated so as to achieve the minimum mean Bayes risk; optimal quantizers are designed by a novel extension to the Lloyd-Max algorithm. It is proven that agents using identical quantizers are not optimal. Thus diversity in the individual agents’ quantizers leads to optimal performance. In addition, for comparison, it is shown how much their performance gets better when information sharing and collaboration among agents before local decision making is allowed.KeywordsDecision RulePrior ProbabilityRepresentation PointFusion CenterFusion RuleThese 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.

A significant problem in physiological state monitoring systems with single data channels is high rates of false alarm. In order to reduce false alarm probability, several data channels can be integrated to enhance system performance. In this work, we have investigated a sensor fusion methodology applicable to physiological state monitoring, which combines local decisions made from dispersed detectors. Difficulties in biophysical signal processing are associated with nonstationary signal patterns and individual characteristics of human physiology resulting in nonidentical observation statistics. Thus a two compartment design, a modified version of well established fusion theory in communication systems, is presented and applied to biological signal processing where we combine discrete wavelet transforms (DWT) with sensor fusion theory. The signals were decomposed in time-frequency domain by discrete wavelet transform (DWT) to capture localized transient features. Local decisions by wavelet power analysis are followed by global decisions at the data fusion center operating under an optimization criterion, i.e., minimum error criterion (MEC). We used three signals acquired from human volunteers exposed to high-G forces at the human centrifuge/dynamic flight simulator facility in Warminster, PA. The subjects performed anti-G straining maneuvers to protect them from the adverse effects of high-G forces. These maneuvers require muscular tensing and altered breathing patterns. We attempted to determine the subject's state by detecting the presence or absence of the voluntary anti-G straining maneuvers (AGSM). During the exposure to high G force the respiratory patterns, blood pressure and electroencephalogram (EEG) were measured to determine changes in the subject's state. Experimental results show that the probability of false alarm under MEC can be significantly reduced by applying the same rule found at local thresholds to all subjects, and MEC can be employed as a robust system to the case of defective/jammed local sensors. This implies the feasibility of our system for physiological state monitoring under a unifying criterion by biological information fusion, and provides significant guidance for algorithm development.

We consider a binary parallel decentralized detection system. It employs n local detectors (LDs) to observe a binary phenomenon in order to accept one of two hypotheses about the phenomenon (hypothesis H 0 or hypothesis H 1 ). Each LD uses a local decision rule to compress its local observations into a binary local decision. The Data Fusion Center (DFC) uses a fusion rule to combine all binary local decisions into a global binary decision. The combination of the global fusion rule and all local decision rules in the system is referred to as a decision strategy. In many scenarios, the system uses a single (deterministic) decision strategy — the DFC used a single deterministic fusion rule and each LD uses a single deterministic decision rule. A randomized strategy involves a randomized or pseudo — randomized choice between several deterministic decision strategies. In some instances, such randomized strategy is needed to ensure that the Receiver Operator Characteristic (ROC) curve of the architecture is convex. We are interested in scenarios that require that the randomized strategy be coordinated between the DFC and the LDs, maintaining synchronization between the selection scheme of local decision rules and global fusion rules. Circumstances that require such coordinated randomized selection are labeled “dependent randomization.” We present systems that use dependent randomization, and also discuss their response when synchronization is occasionally lost.

Although Finite-State Automata (FSA) have been successfully used in modeling and control of Discrete Event Systems (DESs), they are limited to represent complex and advanced features of DESs, such as context recognition and switching. The literature has suggested that a FSA can nevertheless be enriched with parameters properly collected from the modeled system, so that this favors design and control. A parameter can be embedded either on transitions or states. However, each approach is structured within a specific framework, so that their comparison and integration are not straightforward and they may lead to different control solutions, modeled, computed and implemented using distinct strategies. In this paper, we show how to combine advantages from parameters in modeling and control of DESs. Each approach is structured and their advantages are identified and exemplified. Then, we propose a conversion method that allows to translate a design-friendly model into a synthesis-efficient structure. Examples illustrate the approach.

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.

We propose a formalism for decentralized control of discrete event systems with communications. The formalism is based on PN/sup 2/, a class of agent-oriented Petri nets proposed by the author (2001). The main difference between PN/sup 2/ and Petri nets is that each token, representing an agent, is also a Petri net. The decentralized control system to be modeled has the following features: (1) the system is asynchronous and has no global clock; (2) some events may occur concurrently; (3) the system is controlled by several control agents, each of which perceives only a subset of occurring events, and can control only a subset of events; and (4) each control agent can communicate with other agents. By communications, each agent can know occurrences of events that are not observable for it, and can ask other agents to disable events that are not controllable for it. Using the formalism, we define a problem concerning control synthesis.

A modified normality condition for decentralized supervisory control of discrete event systems

Due to the introduction of uncontrollable transitions in the supervisory control of discrete event systems modeled by controlled Petri nets, a disjunction of several linear inequalities is needed to express the admissible markings. In this paper, we propose a two level hierarchical control synthesis method to deal with this kind of OR logic constraints. In the method, the constraint function plays an important role not only in the construction of the low level monitor but also in the determination of the control policy. The obtained supervisor is maximally permissive and the online computation has the complexity of polynomial times. An example is used to illustrate the proposed synthesis algorithm.

In decentralized control of discrete event systems, two main agents contribute to the computation of decisions: local supervisors and fusion modules. The local supervisors process the information detected on the plant and its environment, and transmit their results to the fusion modules. The latter process what is received from the local supervisors in order to decide actions to be applied to the plant. In the existing decentralized control architectures, the local supervisors execute complex operations, while the fusion modules execute simple operations. In the present article, we propose to move the decision computation complexity from local supervisors to fusion modules, that is what we term: moving decisions closer to actions. We justify this movement of decision and develop a simple architecture based on it. With the proposed architecture, the local supervisors are simple local observers, while all decisions are computed by the fusion modules. We characterize the class of languages achievable with the new architecture and compare it with the classes of languages achievable with the existing decentralized architectures and the centralized architecture.