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