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In cyber-physical systems (CPSs), it is of great importance to handle network attack issues. In this article, we consider the supervisory control layer of CPSs, focusing on closed-loop control systems vulnerable to sensor-reading modification attacks (SM-attacks), which may disguise the occurrence of an event as a different event by modifying appropriately sensor readings in sensor communication channels. In particular, we consider the plant modeled as a bounded Petri net and the control specification consisting in liveness enforcing. Based on repeatedly computing a more restrictive liveness-enforcing supervisor under no attack and constructing a so-called basic supervisor, a method that synthesizes a liveness-enforcing supervisor tolerant to an SM-attack is proposed.

This work addresses the robust control problem of discrete event systems assuming that replacement attacks may occur, thus making it appear that an event that has occurred looks like another event. In particular, we assume that this is done by tampering with the sensor-readings in the sensor communication channel. Specifically, we use Petri nets as the reference formalism to model the plant and assume a control specification in terms of a Generalized Mutual Exclusion Constraint. We propose three different methods to derive a control policy that is robust to the possible replacement attacks. The first two methods lead to an optimal (i.e., maximally permissive) policy but are computationally inefficient when applied to large-size systems. On the contrary, the third method computes a policy more efficiently, and reveals more easily implementable in practice. However, this is done at the expense of optimality.

This paper is about state estimation in a timed probabilistic setting. The main contribution is a general procedure to design an observer for computing the probabilities of the states for labeled continuous time Markov models as functions of time, based on a sequence of observations and their associated time stamps that have been collected thus far. Two notions of state consistency with respect to such a timed observation sequence are introduced and related necessary and sufficient conditions are derived. The method is then applied to the detection of cyber-attacks. The plant and the possible attacks are described in terms of a labeled continuous time Markov model that includes both observable and unobservable events, and where each attack corresponds to a particular subset of states. Consequently, attack detection is reformulated as a state estimation problem.

In this note, we focus on labeled Petri nets and formalize two properties, language divergence and marking divergence , discussing their relevance for diagnosability analysis. In particular, we review the results for diagnosability and $K$ -diagnosability presented in an article entitled “A new approach for diagnosability analysis of Petri nets using verifier nets” that we coauthored. We show that these results apply to nets that are language divergence-free, an assumption that was not explicitly mentioned in that article. In addition, we also provide an alternative structural assumption—which does not require testing the behavioral property of divergence-freeness—under which the above results hold.

This article proposes a novel methodology for multistage, multiproduct, multi-item, and closed-loop Supply Chain Network (SCN) design under uncertainty. The method considers that multiple products are manufactured by the SCN, each composed by multiple items, and that some of the sold products may require repair, refurbishing, or remanufacturing activities. We solve the two main decisions that take place in the medium-/short-term planning horizon, namely partners’ selection and allocation of the received orders among them. The partners’ selection problem is solved by a cross-efficiency fuzzy Data Envelopment Analysis technique, which allows evaluating the efficiency of each SCN member and ranking them against multiple conflicting objectives under uncertain data on their performance. Then, according to the estimated customers’ demand, the order allocation problem is solved by a fuzzy bargaining game problem, where each SCN actor behaves to simultaneously maximize both its own profit and the service level of the overall SCN in terms of efficiency, costs, and lead time. An illustrative example from the literature is finally presented. Note to Practitioners —We present a decision tool to address the optimal design, performance evaluation, and continuous improvement of modern cooperative SCNs. We propose an effective method to jointly solve the members’ selection and the orders’ allocation, considering the complex structure of modern SCNs, the multiobjective nature of the problems, and the uncertainty characterizing economic markets. Competition within SCNs stages and cooperation along the chain are considered, with the aim to improve both financial and environmental sustainability, while ensuring the highest service levels to customers.

The problem of stealthy sensor attacks for labeled Petri nets is considered. An operator observes the plant to establish if a set of critical markings has been reached. The attacker can corrupt the sensor channels that transmit the sensor readings, making the operator incapable to establish when a critical marking is reached. We first construct the stealthy attack Petri net that keeps into account the real plant evolutions observed by the attacker and the corrupted plant evolutions observed by the operator. Starting from the reachability graph of the stealthy attack Petri net, an attack structure is defined: it describes all possible attacks. The supremal stealthy attack substructure can be obtained by appropriately trimming the attack structure. An attack function is effective if the supremal stealthy attack substructure contains a state whose first element is a critical marking and the second element is a noncritical marking.

This paper focuses on the detection of cyber-attacks in a timed probabilistic setting. The plant and the possible attacks are described in terms of a labeled continuous time Markov model that includes both observable and unobservable events, and where each attack corresponds to a particular subset of states. Consequently, attack detection is reformulated as a state estimation problem. A verification methodology is described using a parallel-like composition of the Markov model and its logical observer. The construction of this parallel composition allows us to (i) concisely characterize the set of attacks that can be detected based on the sequences of observations they generate, and (ii) compute performance indicators of interest, such as the a priori probability of an undetectable attack, the average detectability, and the mean delay to detection.