VERIFICATION AND APPLICATION OF DETECTABILITY BASED ON PETRI NETS

In many real-world systems, due to limitations of sensors or constraints of the environment, the system dynamics is usually not perfectly known. However, the state information of the system is usually crucial for the purpose of decision making. The state of the system needs to be determined in many applications. Due to its importance, the state estimation problem has received considerable attention in the discrete event system (DES) community. Recently, the state estimation problem has been studied systematically in the framework of detectability. The detectability properties characterize the possibility to determine the current and the subsequent states of a system after the observation of a finite number of events generated by the system. To model and analyze practical systems, powerful DES models are needed to describe the different observation behaviors of the system. Secondly, due to the state explosion problem, analysis methods that rely on exhaustively enumerating all possible states are not applicable for practical systems. It is necessary to develop more efficient and achievable verification methods for detectability. Furthermore, in this thesis, efficient detectability verification methods using Petri nets are investigated, then detectability is extended to a more general definition (C-detectability) that only requires that a given set of crucial states can be distinguished from other states. Formal definitions and efficient verification methods for C-detectability properties are proposed. Finally, C-detectability is applied to the railway signal system to verify the feasibility of this property: 1. Four types of detectability are extended from finite automata to labeled Petri nets. In particular, strong detectability, weak detectability, periodically strong detectability, and periodically weak detectability are formally defined in labeled Petri nets. 2. Based on the notion of basis reachability graph (BRG), a practically efficient approach (the BRG-observer method) to verify the four detectability properties in bounded labeled Petri nets is proposed. Using basis markings, there is no need to enumerate all the markings that are consistent with an observation. It has been shown by other researchers that the size of the BRG is usually much smaller than the size of the reachability graph (RG). Thus, the method improves the analysis efficiency and avoids the state space explosion problem. 3. Three novel approaches for the verification of the strong detectability and periodically strong detectability are proposed, which use three different structures whose construction has a polynomial complexity. Moreover, rather than computing all cycles of the structure at hand, which is NP-hard, it is shown that strong detectability can be verified looking at the strongly connected components whose computation also has a polynomial complexity. As a result, they have lower computational complexity than other methods in the literature. 4. Detectability could be too restrictive in real applications. Thus, detectability is extended to C-detectability that only requires that a given set of crucial states can be distinguished from other states. Four types of C-detectability are defined in the framework of labeled Petri nets. Moreover, efficient approaches are proposed to verify such properties in the case of bounded labeled Petri net systems based on the BRG. 5. Finally, a general modeling framework of railway systems is presented for the states estimation using labeled Petri nets. Then, C-detectability is applied to railway signal systems to verify its feasibility in the real-world system. Taking the RBC handover procedure in the Chinese train control system level 3 (CTCS-3) as an example, the RBC handover procedure is modeled using labeled Petri nets. Then based on the proposed approaches, it is shown that that the RBC handover procedure satisfies strongly C-detectability

On detectability of labeled Petri nets and finite automata

We study detectability properties for labeled Petri nets and finite automata. We first study weak approximate detectability (WAD) that 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 also consider two new concepts called instant strong detectability (ISD) and eventual strong detectability (ESD). The former property implies that for each possible infinite observed output sequence each prefix of the output sequence allows reconstructing the current state. The latter 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. Results: WAD: undecidable for labeled Petri nets, PSPACE-complete for finite automata ISD: decidable and EXPSPACE-hard for labeled Petri nets, belongs to P for finite automata ESD: decidable under promptness assumption and EXPSPACE-hard for labeled Petri nets, belongs to P for finite automata SD: belongs to P for finite automata, strengthens Shu and Lin's 2011 results based on two assumptions of deadlock-freeness and promptness ISD<SD<ESD<WD<WAD for both labeled Petri nets and finite automataComment: 44 pages, 21 figure

On detectability of labeled Petri nets and finite automata

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

Stochastic DES Fault Diagnosis with Coloured Interpreted Petri Nets

[EN] This proposal presents an online method to detect and isolate faults in stochastic discrete event systems without previous model. A coloured timed interpreted Petri Net generates the normal behavior language after an identification stage.The next step is fault detection that is carried out by comparing the observed event sequences with the expected event sequences. Once a new fault is detected, a learning algorithm changes the structure of the diagnoser, so it is able to learn new fault languages. Moreover, the diagnoser includes timed events to represent and diagnose stochastic languages. Finally, this paper proposes a detectability condition for stochastic DES and the sufficient and necessary conditions are proved.This work was supported by a grant from the Universidad del Cauca, Reference 2.3-31.2/05 2011.Muñoz-Añasco, DM.; Correcher Salvador, A.; García Moreno, E.; Morant Anglada, FJ. (2015). Stochastic DES Fault Diagnosis with Coloured Interpreted Petri Nets. 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