arXiv subjects

Alessandro Giua

Publications and source records attributed to Alessandro Giua.

18 recordsLinked to original sources

arXiv2026

Opacity Enforcing Supervisory Control with a Priori Unknown Supervisors

We investigate the enforcement of opacity in discrete-event systems via supervisory control. A system is said to be opaque if a passive intruder can never unambiguously infer whether the system is in a secret state through its observations. In this context, the intruder's knowledge about the supervisor plays a critical role in both problem formulation and solvability. Existing studies typically assume that the policy of the supervisor is either fully unknown to the intruder or fully known a priori, the latter leading to severe technical challenges and unresolved problems under incomparable observations. This paper investigates opacity supervisory control under a new intermediate information setting, which we refer to as the a priori unknown supervisor setting. In this setting, the supervisor's internal realization is not publicly available, but the intruder can partially infer its behavior by eavesdropping on the control decisions issued online during system execution. We formalize the intruder's information-flow under both observation-triggered and decision-triggered decision-issuance mechanisms and define the corresponding notions of opacity. We provide sound and complete algorithms for synthesizing opacity-enforcing supervisors without imposing any restrictions on the observable or controllable event sets. By constructing an information-state structure that embeds the supervisor's estimate of the intruder's belief, the synthesis problem is reduced to a safety game. Finally, we show that, under strictly finer intruder observations, the proposed setting coincides with the standard a priori known supervisor model.

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arXiv2025

On Prediction-Based Properties of Discrete-Event Systems: Notions, Applications and Supervisor Synthesis

In this work, we investigate the problem of synthesizing property-enforcing supervisors for partially-observed discrete-event systems (DES). Unlike most existing approaches, where the enforced property depends solely on the executed behavior of the system, here we consider a more challenging scenario in which the property relies on predicted future behaviors that have not yet occurred. This problem arises naturally in applications involving future information, such as active prediction or intention protection. To formalize the problem, we introduce the notion of prediction-based properties, a new class of observational properties tied to the system's future information. We demonstrate that this notion is very generic and can model various practical properties, including predictability in fault prognosis and pre-opacity in intention security. We then present an effective approach for synthesizing supervisors that enforce prediction-based properties. Our method relies on a novel information structure that addresses the fundamental challenge arising from the dependency between current predictions and the control policy. The key idea is to first borrow information from future instants and then ensure information consistency. This reduces the supervisor synthesis problem to a safety game in the information space. We prove that the proposed algorithm is both sound and complete, and the resulting supervisor is maximally permissive.

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arXiv2025

Probabilistic State Estimation of Timed Probabilistic Discrete Event Systems via Artificial Neural Networks [Draft Version]

This paper is about the state estimation of timed probabilistic discrete event systems. The main contribution is to propose general procedures for developing state estimation approaches based on artificial neural networks. It is assumed that no formal model of the system exists but a data set is available, which contains the history of the timed behaviour of the systems. This dataset will be exploited to develop a neural network model that uses both logical and temporal information gathered during the functioning of the system as inputs and provides the state probability vector as output. Two main approaches are successively proposed (i) state estimation of timed probabilistic discrete event systems over observations: in this case the state estimate is reconstructed at the occurrence of each new observation; (ii) state estimation of timed probabilistic discrete event systems over time: in this case the state estimate is reconstructed at each clock time increment. For each approach, the paper outlines the process of data preprocessing, model building and implementation. This paper not only proposes groundbreaking approaches but also opens the door to further exploitation of artificial neural networks for the benefit of discrete event systems.

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arXiv2025

A Stackelberg Game Approach for Signal Temporal Logic Control Synthesis with Uncontrollable Agents

In this paper, we investigate the control synthesis problem for Signal Temporal Logic (STL) specifications in the presence of uncontrollable agents. Existing works mainly address this problem in a robust control setting by assuming the uncontrollable agents are adversarial and accounting for the worst-case scenario. While this approach ensures safety, it can be overly conservative in scenarios where uncontrollable agents have their own objectives that are not entirely opposed to the system's goals. Motivated by this limitation, we propose a new framework for STL control synthesis within the Stackelberg game setting. Specifically, we assume that the system controller, acting as the leader, first commits to a plan, after which the uncontrollable agents, acting as followers, take a best response based on the committed plan and their own objectives. Our goal is to synthesize a control sequence for the leader such that, for any rational followers producing a best response, the leader's STL task is guaranteed to be satisfied. We present an effective solution to this problem by transforming it into a single-stage optimization problem and leveraging counter-example guided synthesis techniques. We demonstrate that the proposed approach is sound and identify conditions under which it is optimal. Simulation results are also provided to illustrate the effectiveness of the proposed framework.

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arXiv2024

State estimation of timed automata under partial observation [Draft version]

In this paper, we consider partially observable timed automata endowed with a single clock. A time interval is associated with each transition specifying at which clock values it may occur. In addition, a resetting condition associated to a transition specifies how the clock value is updated upon its occurrence. This work deals with the estimation of the current state given a timed observation, i.e., a succession of pairs of an observable event and the time instant at which the event has occurred. The problem of state reachability in the timed automaton is reduced to the reachability analysis of the associated zone automaton, which provides a purely discrete event description of the behaviour of the timed automaton. An algorithm is formulated to provide an offline approach for state estimation of a timed automaton based on the assumption that the clock is reset upon the occurrence of each observable transition.

cs.FL↗

arXiv2024

[Draft] High-order estimation-based properties and high-order observers for labeled finite-state automata

In this paper, we consider labeled finite-state automata (LFSAs), extend some state estimation-based properties from a single agent to a finite ordered set of agents. We also extend the notion of observer to \emph{high-order observer} using our \emph{concurrent composition}. As a result, a general framework for characterizing high-order estimation-based properties is built, in which each agent infers its preceding agent's estimation via all agents in front. The high-order observer plays the role of a basic tool to verify such properties. In more detail, in our general framework, the system's structure is publicly known to all agents $A_1,\dots,A_n$; each agent $A_i$ has its own observable event set $E_i$, and additionally knows all its preceding agents' observable events but can only observe its own observable events. The intuitive meaning of our high-order observer is to characterize what agent $A_n$ knows about what $A_{n-1}$ knows about \dots what $A_2$ knows about $A_1$'s state estimate of the system. This general framework can be regarded as an automata representation of dynamic epistemic logic. Compared with the classical representation of dynamic epistemic logic based on fragments of logic, our representation has advantages in property verification and flexibly changing agents to enforce properties. As case studies, this general framework applies to basic properties such as current-state opacity, strong current-state opacity, regular-language-based opacity, critical observability, high-order opacity, etc. Special cases for which verification can be done more efficiently are also discussed.

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arXiv2024

Algebraic Connectivity Control and Maintenance in Multi-Agent Networks under Attack

This paper studies the problem of increasing the connectivity of an ad-hoc peer-to-peer network subject to cyber-attacks targeting the agents in the network. The adopted strategy involves the design of local interaction rules for the agents to locally modify the graph topology by adding and removing links with neighbors. Two distributed protocols are presented to boost the algebraic connectivity of the network graph beyond $k-2\sqrt{k-1}$ where $k\in \mathbb{N}$ is a free design parameter; these two protocols are achieved through the distributed construction of random (approximate) regular graphs. One protocol leverages coordinated actions between pairs of neighboring agents and is mathematically proven to converge to the desired graph topology. The other protocol relies solely on the uncoordinated actions of individual agents and it is validated by a spectral analysis through Monte-Carlo simulations. Numerical simulations offer a comparative analysis with other state-of-the-art algorithms, showing the ability of both proposed protocols to maintain high levels of connectivity despite attacks carried out with full knowledge of the network structure, and highlighting their superior performance.

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arXiv2023

Novel Stability Conditions for Nonlinear Monotone Systems and Consensus in Multi-Agent Networks

In this work, we characterize a class of nonlinear monotone dynamical systems that have a certain translation invariance property which goes by the name of plus-homogeneity; usually called "topical" systems. Such systems need not be asymptotically stable, since they are merely nonexpansive but not contractive. Thus, we introduce a stricter version of monotonicity, termed "type-K" in honor of Kamke, and we prove the asymptotic stability of the equilibrium points, as well as the convergence of all trajectories to such equilibria for type-K monotone and plus-homogeneous systems: we call them "K-topical". Since topical maps are the natural nonlinear counterpart of linear maps defined by row-stochastic matrices, which are a cornerstone in the convergence analysis of linear multi-agent systems (MASs), we exploit our results for solving the consensus problem over nonlinear K-topical MASs. We first provide necessary and sufficient conditions on the local interaction rules of the agents ensuring the K-topicality of a MAS. Then, we prove that the agents achieve consensus asymptotically if the graph describing their interactions contains a globally reachable node. Finally, several examples for continuous-time and discrete-time systems are discussed to corroborate the enforceability of our results in different applications.

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arXiv2022

You Don't Know What I Know: On Notion of High-Order Opacity in Discrete-Event Systems

In this paper, we investigate a class of information-flow security properties called opacity in partial-observed discrete-event systems. Roughly speaking, a system is said to be opaque if the intruder, which is modeled by a passive observer, can never determine the "secret" of the system for sure. Most of the existing notions of opacity consider secrets related to the actual behaviors of the system. In this paper, we consider a new type of secret related to the knowledge of the system user. Specifically, we assume that the system user also only has partial observation of the system and has to reason the actual behavior of the system. We say a system is high-order opaque if the intruder can never determine that the system user knows some information of importance based on its own incomparable information. We provide the formal definition of high-order opacity. Two algorithms are provided for the verification of this new notion: one with doubly-exponential complexity for the worst case and the other with single-exponential complexity. Illustrative examples are provided for the new notion of high-order opacity.

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arXiv2021

Joint State Estimation Under Attack of Discrete Event Systems

The problem of state estimation in the setting of partially-observed discrete event systems subject to cyber attacks is considered. An operator observes a plant through a natural projection that hides the occurrence of certain events. The objective of the operator is that of estimating the current state of the system. The observation is corrupted by an attacker which can tamper with the readings of a set of sensors thus inserting some fake events or erasing some observations. The aim of the attacker is that of altering the state estimation of the operator. An automaton, called joint estimator, is defined to describe the set of all possible attacks. In more details, an unbounded joint estimator is obtained by concurrent composition of two state observers, the attacker observer and the operator observer. The joint estimator shows, for each possible corrupted observation, the joint state estimation, i.e., the set of states consistent with the uncorrupted observation and the set of states consistent with the corrupted observation. Such a structure can be used to establish if an attack function is harmful w.r.t. a misleading relation. Our approach is also extended to the case in which the attacker may insert at most n events between two consecutive observations.

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arXiv2021

Non-Blockingness Verification of Bounded Petri Nets Using Basis Reachability Graphs -- An Extended Version With Benchmarks

In this paper, we study the problem of non-blockingness verification by tapping into the basis reachability graph (BRG). Non-blockingness is a property that ensures that all pre-specified tasks can be completed, which is a mandatory requirement during the system design stage. In this paper we develop a condition of transition partition of a given net such that the corresponding conflict-increase BRG contains sufficient information on verifying non-blockingness of its corresponding Petri net. Thanks to the compactness of the BRG, our approach possesses practical efficiency since the exhaustive enumeration of the state space can be avoided. In particular, our method does not require that the net is deadlock-free.

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arXiv2020

Dynamic Max-Consensus and Size Estimation of Anonymous Multi-Agent Networks

In this paper we propose a novel consensus protocol for discrete-time multi-agent systems (MAS), which solves the dynamic consensus problem on the max value, i.e., the dynamic max-consensus problem. In the dynamic max-consensus problem to each agent is fed a an exogenous reference signal, the objective of each agent is to estimate the instantaneous and time-varying value of the maximum among the signals fed to the network, by exploiting only local and anonymous interactions among the agents. The absolute and relative tracking error of the proposed distributed control protocol is theoretically characterized and is shown to be bounded and by tuning its parameters it is possible to trade-off convergence time for steady-state error. The dynamic Max-consensus algorithm is then applied to solve the distributed size estimation problem in a dynamic setting where the size of the network is time-varying during the execution of the estimation algorithm. Numerical simulations are provided to corroborate the theoretical analysis.

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arXiv2020

A framework for the analysis of supervised discrete event systems under attack

This paper focuses on the problem of cyber attacks for discrete event systems under supervisory control. In more detail, the goal of the supervisor, who has a partial observation of the system evolution, is that of preventing the system from reaching a set of unsafe states. An attacker may act in two different ways: he can corrupt the observation of the supervisor editing the sensor readings, and can enable events that are disabled by the supervisor. This is done with the aim of leading the plant to an unsafe state, and keeping the supervisor unaware of that before the unsafe state is reached. A special automaton, called attack structure is constructed as the parallel composition of two special structures. Such an automaton can be used by the attacker to select appropriate actions (if any) to reach the above goal, or equivalently by the supervisor, to validate its robustness with respect to such attacks.

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arXiv2020

Verification of Nonblockingness in Bounded Petri Nets With Minimax Basis Reachability Graphs

This paper proposes a semi-structural approach to verify the nonblockingness of a Petri net. We construct a structure, called minimax basis reachability graph (minimax-BRG): it provides an abstract description of the reachability set of a net while preserving all information needed to test if the net is blocking. We prove that a bounded deadlock-free Petri net is nonblocking if and only if its minimax-BRG is unobstructed, which can be verified by solving a set of integer constraints and then examining the minimax-BRG. For Petri nets that are not deadlock-free, one needs to determine the set of deadlock markings. This can be done with an approach based on the computation of maximal implicit firing sequences enabled by the markings in the minimax-BRG. The approach we developed does not require the construction of the reachability graph and has wide applicability.

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arXiv2019

Revisiting delayed strong detectability of discrete-event systems

Among notions of detectability for a discrete-event system (DES), strong detectability implies that after a finite number of observations to every output/label sequence generated by the DES, the current state can be uniquely determined. This notion is strong so that by using it the current state can be easily determined. In order to keep the advantage of strong detectability and weaken its disadvantage, we can additionally take some "subsequent outputs" into account in order to determine the current state. Such a modified observation will make some DES that is not strongly detectable become "strongly detectable in a weaker sense", which we call "{\it $K$-delayed strong detectability}" if we observe at least $K$ outputs after the time at which the state need to be determined. In this paper, we study $K$-delayed strong detectability for DESs modeled by finite-state automata (FSAs), and give a polynomial-time verification algorithm by using a novel concurrent-composition method. Note that the algorithm applies to all FSAs. Also by the method, an upper bound for $K$ has been found, and we also obtain polynomial-time verification algorithms for $(k_1,k_2)$-detectability and $(k_1,k_2)$-D-detectability of FSAs firstly studied by [Shu and Lin, 2013]. Our algorithms run in quartic polynomial time and apply to all FSAs, are more effective than the sextic polynomial-time verification algorithms given by [Shu and Lin 2013] based on the usual assumptions of deadlock-freeness and having no unobservable reachable cycle. Finally, we obtain polynomial-time synthesis algorithms for enforcing delayed strong detectability, which are more effective than the exponential-time synthesis algorithms in the supervisory control framework in the literature.

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arXiv2019

A Nonlinear Perron-Frobenius Approach for Stability and Consensus of Discrete-Time Multi-Agent Systems

In this paper we propose a novel method to establish stability and, in addition, convergence to a consensus state for a class of discrete-time Multi-Agent System (MAS) evolving according to nonlinear heterogeneous local interaction rules which is not based on Lyapunov function arguments. In particular, we focus on a class of discrete-time MASs whose global dynamics can be represented by sub-homogeneous and order-preserving nonlinear maps. This paper directly generalizes results for sub-homogeneous and order-preserving linear maps which are shown to be the counterpart to stochastic matrices thanks to nonlinear Perron-Frobenius theory. We provide sufficient conditions on the structure of local interaction rules among agents to establish convergence to a fixed point and study the consensus problem in this generalized framework as a particular case. Examples to show the effectiveness of the method are provided to corroborate the theoretical analysis.

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arXiv2019

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 automata

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arXiv2012

Decentralized Estimation of Laplacian Eigenvalues in Multi-Agent Systems

In this paper we present a decentralized algorithm to estimate the eigenvalues of the Laplacian matrix that encodes the network topology of a multi-agent system. We consider network topologies modeled by undirected graphs. The basic idea is to provide a local interaction rule among agents so that their state trajectory is a linear combination of sinusoids oscillating only at frequencies function of the eigenvalues of the Laplacian matrix. In this way, the problem of decentralized estimation of the eigenvalues is mapped into a standard signal processing problem in which the unknowns are the finite number of frequencies at which the signal oscillates.

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