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Kuize Zhang - One of the best experts on this subject based on the ideXlab platform.
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On Detectability of labeled Petri nets and finite automata
Discrete Event Dynamic Systems, 2020Co-Authors: Kuize Zhang, Alessandro GiuaAbstract:Detectability is a basic property of dynamic systems: when it holds an observer can use the current and past values of the observed output signal produced by a system to reconstruct its current state. In this paper, we consider properties of this type in the framework of discrete-event systems modeled by labeled Petri nets and finite automata. We first study weak approximate Detectability . This property implies that there exists an infinite observed output sequence of the system such that each prefix of the output sequence with length greater than a given value allows an observer to determine if the current state belongs to a given set. We prove that the problem of verifying this property is undecidable for labeled Petri nets, and PSPACE-complete for finite automata. We also consider one new concept called eventual strong Detectability . The new property implies that for each possible infinite observed output sequence, there exists a value such that each prefix of the output sequence with length greater than that value allows reconstructing the current state. We prove that for labeled Petri nets, the problem of verifying eventual strong Detectability is decidable and EXPSPACE-hard, where the decidability result holds under a mild promptness assumption. For finite automata, we give a polynomial-time verification algorithm for the property. In addition, we prove that strong Detectability is strictly stronger than eventual strong Detectability for labeled Petri nets and even for deterministic finite automata.
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A unified method to decentralized state inference and fault diagnosis/prediction of discrete-event systems.
arXiv: Optimization and Control, 2020Co-Authors: Kuize ZhangAbstract:The state inference problem and fault diagnosis/prediction problem are fundamental topics in many areas. In this paper, we consider discrete-event systems (DESs) modeled by finite-state automata (FSAs). There exist results for decentralized versions of the latter problem but there is almost no result for a decentralized version of the former problem. We propose a decentralized version of strong Detectability called co-Detectability which implies that once a system satisfies this property, for each generated infinite-length event sequence, at least one local observer can determine the current and subsequent states after a common observation time delay. We prove that the problem of verifying co-Detectability of FSAs is coNP-hard. Moreover, we use a unified concurrent-composition method to give PSPACE verification algorithms for co-Detectability, co-diagnosability, and co-predictability of FSAs, without any assumption or modifying the FSAs under consideration, where co-diagnosability is firstly studied by [Debouk & Lafortune & Teneketzis 2000], while co-predictability is firstly studied by [Kumar \& Takai 2010]. By our proposed unified method, one can see that in order to verify co-Detectability, more technical difficulties will be met compared to verifying the other two properties, because in co-Detectability, generated outputs are counted, but in the latter two properties, only occurrences of events are counted. For example, when one output was generated, any number of unobservable events could have occurred. The PSPACE-hardness of verifying co-diagnosability is already known in the literature. In this paper, we prove the PSPACE-hardness of verifying co-predictability.
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the problem of determining the weak periodic Detectability of discrete event systems is pspace complete
Automatica, 2017Co-Authors: Kuize ZhangAbstract:Abstract In Shu and Lin, 2011, exponential time (actually polynomial space) algorithms for determining the weak Detectability and weak periodic Detectability of nondeterministic discrete event systems (DESs) are designed. In this paper, we prove that the problems of determining the weak Detectability and weak periodic Detectability of deterministic DESs are both PSPACE-hard (hence PSPACE-complete). Then as corollaries, the problems of determining the weak Detectability and weak periodic Detectability of nondeterministic DESs are also PSPACE-hard (hence PSPACE-complete).
Feng Lin - One of the best experts on this subject based on the ideXlab platform.
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Detectability of networked discrete event systems
Discrete Event Dynamic Systems, 2018Co-Authors: Yazeed Sasi, Feng LinAbstract:Detectability of discrete event systems, defined as the ability to determine the current and subsequent states, is very important in diagnosis, control, and many other applications. So far only Detectability of non-networked discrete event systems has been defined and investigated. Non-networked discrete event systems assume that all the communications are reliable and instantaneous without any delays or losses. This assumption is often violated in networked systems. In this paper, we study Detectability for networked discrete event systems. We investigate the impact of communication delays and losses on Detectability. We define two classes of detectabilities: network Detectability for determining the state of a networked discrete event systems and network D-Detectability for distinguishing certain pairs of states of the systems. Necessary and sufficient conditions for network Detectability and network D-Detectability are derived. Methods to check network Detectability and network D-Detectability are also developed. Examples are given to illustrate the results.
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I-Detectability of Discrete-Event Systems
IEEE Transactions on Automation Science and Engineering, 2013Co-Authors: Shaolong Shu, Feng LinAbstract:State estimation has always been important in discrete-event systems. There are two types of state estimation problems in discrete-event systems: one is to determine the initial state of the system and the other is to determine the current state of the system. In this paper, we investigate the initial state estimation problem. We formulate initial state estimation problem as I-Detectability. A discrete-event system is strongly I-detectable if we can determine the initial state of the system after a finite number of event observations for all trajectories of the system. It is weakly I-detectable if we can determine the initial state of the system for some trajectories of the system. We construct I-observer to analyze strong and weak I-Detectability and construct I-detector to check strong I-Detectability. For some applications, strong I-Detectability is required but not satisfied; hence we investigated how to control a system to achieve strong I-Detectability if needed. If there exists a controllable, observable, and strongly I-detectable sublanguage, then we say the system is closed-loop strongly I-detectable. We derive an effective algorithm to check whether a system is closed-loop strongly I-detectable. The algorithm can also calculate a controllable, observable, and strongly I-detectable sublanguage if the system is closed-loop strongly I-detectable.
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Generalized Detectability for discrete event systems
Systems & control letters, 2011Co-Authors: Shaolong Shu, Feng LinAbstract:In our previous work, we investigated Detectability of discrete event systems, which is defined as the ability to determine the current and subsequent states of a system based on observation. For different applications, we defined four types of detectabilities: (weak) Detectability, strong Detectability, (weak) periodic Detectability, and strong periodic Detectability. In this paper, we extend our results in three aspects. (1) We extend Detectability from deterministic systems to nondeterministic systems. Such a generalization is necessary because there are many systems that need to be modeled as nondeterministic discrete event systems. (2) We develop polynomial algorithms to check strong Detectability. The previous algorithms are based on observer whose construction is of exponential complexity, while the new algorithms are based on a new automaton called detector. (3) We extend Detectability to D-Detectability. While Detectability requires determining the exact state of a system, D-Detectability relaxes this requirement by asking only to distinguish certain pairs of states. With these extensions, the theory on Detectability of discrete event systems becomes more applicable in solving many practical problems.
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Detectability of Discrete Event Systems
IEEE Transactions on Automatic Control, 2007Co-Authors: Shaolong Shu, Feng Lin, Hao YingAbstract:In this note, we investigate the Detectability problem in discrete event systems. We assume that we do not know initially which state the system is in. The problem is to determine the current and subsequent states of the system based on a sequence of observations. The observation includes partial event observation and/or partial state observation, which leads to four possible cases. We further define four types of detectabilities: strong Detectability, (weak) Detectability, strong periodic Detectability, and (weak) periodic Detectability. We derive necessary and sufficient conditions for these detectabilities. These conditions can be checked by constructing an observer, which models the estimation of states under different observations. The theory developed in this note can be used in feedback control and diagnosis. If the system is detectable, then the observer can be used as a diagnoser to diagnose the failure states of the system.
Shaolong Shu - One of the best experts on this subject based on the ideXlab platform.
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I-Detectability of Discrete-Event Systems
IEEE Transactions on Automation Science and Engineering, 2013Co-Authors: Shaolong Shu, Feng LinAbstract:State estimation has always been important in discrete-event systems. There are two types of state estimation problems in discrete-event systems: one is to determine the initial state of the system and the other is to determine the current state of the system. In this paper, we investigate the initial state estimation problem. We formulate initial state estimation problem as I-Detectability. A discrete-event system is strongly I-detectable if we can determine the initial state of the system after a finite number of event observations for all trajectories of the system. It is weakly I-detectable if we can determine the initial state of the system for some trajectories of the system. We construct I-observer to analyze strong and weak I-Detectability and construct I-detector to check strong I-Detectability. For some applications, strong I-Detectability is required but not satisfied; hence we investigated how to control a system to achieve strong I-Detectability if needed. If there exists a controllable, observable, and strongly I-detectable sublanguage, then we say the system is closed-loop strongly I-detectable. We derive an effective algorithm to check whether a system is closed-loop strongly I-detectable. The algorithm can also calculate a controllable, observable, and strongly I-detectable sublanguage if the system is closed-loop strongly I-detectable.
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Generalized Detectability for discrete event systems
Systems & control letters, 2011Co-Authors: Shaolong Shu, Feng LinAbstract:In our previous work, we investigated Detectability of discrete event systems, which is defined as the ability to determine the current and subsequent states of a system based on observation. For different applications, we defined four types of detectabilities: (weak) Detectability, strong Detectability, (weak) periodic Detectability, and strong periodic Detectability. In this paper, we extend our results in three aspects. (1) We extend Detectability from deterministic systems to nondeterministic systems. Such a generalization is necessary because there are many systems that need to be modeled as nondeterministic discrete event systems. (2) We develop polynomial algorithms to check strong Detectability. The previous algorithms are based on observer whose construction is of exponential complexity, while the new algorithms are based on a new automaton called detector. (3) We extend Detectability to D-Detectability. While Detectability requires determining the exact state of a system, D-Detectability relaxes this requirement by asking only to distinguish certain pairs of states. With these extensions, the theory on Detectability of discrete event systems becomes more applicable in solving many practical problems.
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Detectability of Discrete Event Systems
IEEE Transactions on Automatic Control, 2007Co-Authors: Shaolong Shu, Feng Lin, Hao YingAbstract:In this note, we investigate the Detectability problem in discrete event systems. We assume that we do not know initially which state the system is in. The problem is to determine the current and subsequent states of the system based on a sequence of observations. The observation includes partial event observation and/or partial state observation, which leads to four possible cases. We further define four types of detectabilities: strong Detectability, (weak) Detectability, strong periodic Detectability, and (weak) periodic Detectability. We derive necessary and sufficient conditions for these detectabilities. These conditions can be checked by constructing an observer, which models the estimation of states under different observations. The theory developed in this note can be used in feedback control and diagnosis. If the system is detectable, then the observer can be used as a diagnoser to diagnose the failure states of the system.
Weihai Zhang - One of the best experts on this subject based on the ideXlab platform.
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On stability and Detectability of complex stochastic systems
2012 24th Chinese Control and Decision Conference (CCDC), 2012Co-Authors: Weihai Zhang, Cheng TanAbstract:Stability and Detectability of stochastic systems are essential and important concepts in control theory which have been a popular research direction in recent years. However, most study about stability and Detectability are concentrated on real stochastic systems instead of complex stochastic systems. In this paper, the matrix transformation approach is used to study asymptomatical mean square stability, critical stability, D-stability and Detectability of continuous-time complex stochastic systems. With the aid of the spectral analysis technique, we can obtain some practical criteria for stability and detectabilit. Moreover, some useful properties of the generalized Lyapunov equation are derived based on critical stability and exact Detectability of complex stochastic systems.
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generalized lyapunov equation approach to state dependent stochastic stabilization Detectability criterion
IEEE Transactions on Automatic Control, 2008Co-Authors: Weihai Zhang, Huanshui Zhang, Borsen ChenAbstract:In this paper, the generalized Lyapunov equation approach is used to study stochastic stabilization/Detectability with state-multiplicative noise. Some practical test criteria for stochastic stabilization and Detectability, such as stochastic Popov-Belevitch-Hautus criterion for exact Detectability, are obtained. Moreover, useful properties of the generalized Lyapunov equation are derived based on critical stability and exact Detectability introduced in this paper. As applications, first, the stochastic linear quadratic regulator as well as the related generalized algebraic Riccati equation are discussed extensively. Second, the infinite horizon stochastic H 2/H infin control with state- and control-dependent noise is also investigated, which extends and improves the recently published results.
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A Note on Detectability of Stochastic Systems with Application
2006 Chinese Control Conference, 2006Co-Authors: Weihai ZhangAbstract:This note has clarified the relation among stochastic Detectability, exact Detectability and complete Detectability via some examples. It is shown that stochastic Detectability implies both exact Detectability and complete Detectability, but the converse is not true. applying exact Detectability to the study of stochastic LQ optimal control, the previous results are improved.
Alessandro Giua - One of the best experts on this subject based on the ideXlab platform.
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Verification of Detectability for Unambiguous Weighted Automata
IEEE Transactions on Automatic Control, 2021Co-Authors: Aiwen Lai, Sébastien Lahaye, Alessandro GiuaAbstract:In this article, we deal with the Detectability problem for unambiguous weighted automata (UWAs). The problem is to determine if, after a finite number of observations, the set of possible states is reduced to a singleton. Four types of detectabilities, namely, strong Detectability, Detectability, strong periodic Detectability, and periodic Detectability are defined in terms of different requirements for current state estimation. We first construct a deterministic finite state automaton (called observer) over a weighted alphabet and prove that it can be used as the current-state estimator of the studied UWA. Finally, necessary and sufficient conditions based on the observer are proposed to verify detectabilities of a UWA.
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On Detectability of labeled Petri nets and finite automata
Discrete Event Dynamic Systems, 2020Co-Authors: Kuize Zhang, Alessandro GiuaAbstract:Detectability is a basic property of dynamic systems: when it holds an observer can use the current and past values of the observed output signal produced by a system to reconstruct its current state. In this paper, we consider properties of this type in the framework of discrete-event systems modeled by labeled Petri nets and finite automata. We first study weak approximate Detectability . This property implies that there exists an infinite observed output sequence of the system such that each prefix of the output sequence with length greater than a given value allows an observer to determine if the current state belongs to a given set. We prove that the problem of verifying this property is undecidable for labeled Petri nets, and PSPACE-complete for finite automata. We also consider one new concept called eventual strong Detectability . The new property implies that for each possible infinite observed output sequence, there exists a value such that each prefix of the output sequence with length greater than that value allows reconstructing the current state. We prove that for labeled Petri nets, the problem of verifying eventual strong Detectability is decidable and EXPSPACE-hard, where the decidability result holds under a mild promptness assumption. For finite automata, we give a polynomial-time verification algorithm for the property. In addition, we prove that strong Detectability is strictly stronger than eventual strong Detectability for labeled Petri nets and even for deterministic finite automata.
